It is the day after the Queen Mother's funeral, and Their Royal Highnesses the Earl and Countess of Wessex are back at work opening a school sports hall in Dorking, the soft centre of Surrey. Before an audience of 200 staff, pupils, governors and worthies, Prince Edward takes the stage, makes a brief speech thanking everyone for their efforts, then turns with practised ease to a pair of small, velvet curtains concealing a plaque. "Now," he says, grasping the drawstring with exaggerated care, "I'm going to make this look as easy as possible, but I want you to know it's taken years of practice." It's a good gag, and it gets a hearty laugh - for the second time today. He used the same line when opening Caterham police station in the morning. If the Wessexes are serious about their new careers as full-time royals, the routine is going to need a bit more variety.

Recycled jokes aside, the day's events are something of a palace coup. Basking in spring sunshine and the afterglow of the previous day's ceremonials, the couple, still dressed in funereal black, are greeted with sympathy and smiles from Caterham to Dorking via Redhill. The message for the media, lapped up by rolling news channels and the lunchtime TV bulletins, is clear: they may be in mourning, but it's business as usual for the hard-working Wessexes. Given the parlous state of their relations with the media, such positive coverage is rare. For those overseeing the rebranding of the most reviled members of the royal family, it is a minor triumph.

The overhaul of the Wessexes' image follows the announcement seven weeks ago that they were abandoning their commercial roles to take up full-time royalling. It was a decision that neither apparently relished, but the relief at the palace was as palpable as the scorn in the tabloids. In jubilee year the couple's commercial exploits looked increasingly like a disaster waiting to happen.

So three months after losing her first child to an ectopic pregnancy, Sophie left her moderately successful PR company in favour of a career that, in the short term at least, involves receiving posies from gap-toothed children and listening to her husband tell reheated jokes. In the past month it has taken her the length of the UK, from Kent to Dundee. Following yesterday's engagements in Manchester, today they fly to the US, where they will visit New York, Washington and Los Angeles. Nice work if you can get it.

For Edward the retreat to public life is surely more galling. Had things worked out differently, the seventh in line to the throne might now be hunting al-Qaida with the Royal Marines in the Afghan mountains. Instead, approaching 40, he is surveying the ruins of a failed television company and the prospect of returning to a career that he has spent his whole adult life trying to avoid. His grandmother, apparently infused with the virtues of service and duty, viewed the dull-but-worthy chores of royalling as the price of a lifestyle of imperial luxury. Edward, a man apparently seduced by showbiz since his teens, now has the opportunity to demonstrate that he and his wife appreciate that there is a payoff.

Whatever their private resentments, there is a concerted effort under way to portray them as hard-working, worthwhile members of the family. (This does not go as far as granting interviews on the subject, a reticence that contrasts with Edward's willingness in the past to grant audiences to promote his latest television productions.)

But what constitutes hard work? Even the newly sure-footed palace press operation, so adept in its handling of the Queen Mother's obsequies, will struggle to convince anyone that the sparse work in their official diary is worth a salary approaching £250,000 a year.

When the Wessexes announced in March that they were going full time, their diary listed 21 domestic engagements to the end of July, a figure exceeded by all the working royals except Princess Alexandra. That has since increased to 26, excluding funeral duties and this week's trip to the US.

In the past seven weeks they have fulfilled four full days of engagements in Kent, Newcastle, Surrey and Manchester, and attended three concerts, four schools, a play, a ballet and several charity dinners. By the time the Commonwealth Games open in Manchester in late July - Edward will attend them every day for a fortnight - they will have done 14 days' work in five months, excluding trips and funeral duties.

The cost of keeping the couple on - and more frequently off - the road is less clear. Edward will soon receive a rise in his civil-list salary from £141,000 to £249,000 as the couple increase the size of their private office to cope with the anticipated extra workload. The Queen reimburses the money but, at 38, Edward can take little pride in living off his mother.

In addition to the cost of the private office, each engagement is reconnoitred and staffed by at least one press officer, two royal protection squad officers, a driver and numerous local special branch and uniformed police officers. Add the use of vehicles and the royal flight, which yesterday whisked them from Uxbridge to Manchester, and the cost of unveiling a plaque approaches five figures.

Uncertainty also surrounds the future of Bagshot Park, the couple's Surrey mansion. The palace say they have no plans to move "at the moment", but it remains to be seen whether Edward's allowance, plus the interest from his estimated £7m private fortune, will be sufficient to meet the annual running costs of £2m. (In a neat irony, one barrier to them downsizing is the 50-year lease that Edward took out with Bagshot Park's owners, the Crown Estates. The civil list on which he now relies was devised by parliament to reimburse the royals when they handed over the income from the Crown Estates.)

The palace insists that their diary will fill up in the coming months. Edward will continue to pursue his interests in the arts through patronage - yesterday he attended a fundraising lunch at the Royal Exchange theatre in Manchester, where he met Amanda Donohoe.

Sophie, increasingly viewed as an unexploited asset rather than a liability, will take on patronages in her own right. (Last Saturday she did her first solo engagement, opening a spring fair not far from home in Surrey.) Judging by her work over the past month, it seems that the palace's faith is not misplaced. She has an easy way with the nervous, manages to look interested all day, and bears the weight of the attention lightly. Aides say she took media coverage of the loss of her child very hard, particularly a story alleging that she was seeking IVF treatment, but speak of her courtesy and charm.

The palace still receives thousands of requests for royal visits and, in an ageing family, the relatively youthful Wessexes need not be short of work. And by those works, runs the palace line, we shall know them. In the sports hall in Dorking, an aide tells an anecdote that typifies the image they are striving for.

"The countess came in to see me not long ago, the day after the Daily Mail had run a piece saying she wanted to be the new Diana. 'This just isn't true,' she said. 'I want to be thought of like the Princess Royal - she gets judged on the work she does.' They're going to get their heads down, work hard, and they really want to make a success of this. They're really determined."

The comparison with Princess Anne (172 engagements to the end of July) is telling. She receives less flak than any of the royal divorcees, chiefly because of her huge workload. She may be stern, but she has unveiled so many plaques that it's a wonder she can pass a pair of curtains without opening them and saying a few words of congratulation.

The Wessexes have an enormous way to go before they match that workload, and the enviably low profile that goes with it, but thanks to the Queen Mother's demise they now have some breathing space. (This in spite of the unfortunate reminder of Edward's military record that it provided. While his brothers and sister strode in uniform behind the coffin as it was processed to Westminster Hall, he was in a morning suit. The only other grandson similarly dressed was Lord Linley, a furniture designer.)

For a while at least, open season has been called off, and the Surrey roadshow demonstrated a reservoir of goodwill that they will seek to exploit. By "bravely" meeting their diary commitments they earned the thanks and respect of all they encountered.

In Newcastle three weeks earlier, however, the hostility generated by a decade of bad publicity and crass conduct was evident. This was the reality of full-time royalling: cold winds, sparse crowds, grubby sports centres, subjects struck dumb with apprehension, and dignitaries in their best suits jostling for position in receiving lines. The day's engagements were all connected to the Duke of Edinburgh's Award scheme, of which Edward is a patron, and began at Firfield community school, which a few years ago resorted to paying pupils to attend. In July the school will merge with another in the city in search of a fresh start. For staff and pupils the visit was recognition of their work to turn it round.

"Ooh, she looks good today," whispered a teacher, admiring the Countess's navy twinset as she emerged from a BMW at the school gates. He is slimmer than one expects, slight even, and thinning faster than his elder brothers.

They move along the reception line, shaking hands and nodding. Sophie appears relaxed and easy-going, a sort of Diana-lite. Edward, however, carries the curse of the family's men; he looks like he has been starched from the collar up and walks with the Windsor armlock (left arm behind back, right hand holding left forearm) practised by his brothers and father. As he is introduced to the headmaster, he nervously rises slowly on to the balls of his feet. "Right then, shall we go and have a look at some of the young people you've got here?" he suggests.

In the assembly hall, Edward delivers a pleasant, vaguely inspirational speech spoilt by an ill-judged and almost incomprehensible anecdote that attempts to draw a parallel between orienteering trips at Gordonstoun and day trips from a Newcastle sink school. In common with most of the staff and pupils, Lyndsay Bell, 16, doesn't care about this lapse. "It was good meeting them," she says. "It's good them coming here, good that they picked this school, what with it closing and everything."

Later, outside the North Shields YMCA, the modest crowd waiting for the Wessexes to arrive is far less forgiving. North Shields is loyal old Labour territory - the sort of place you would expect to find residual support for the royals; but not according to the three dozen or so people who have interrupted their shopping - or bunking-off - to await the couple's arrival, or to the callers to Radio Newcastle's morning phone-in, who agree with the proposition that the monarchy should be downsized. Here the sterotypes of the Wessexes hold good.

"It's good publicity for the YMCA, them coming. But I think the majority of the country don't believe in the royal family any more," says Carl Betsford, a YMCA steward.

Jemma Thompson, Mandy Craggs and Stacey Weatherstone, all 15 and claiming that they aren't playing truant, are less circumspect. "We think he's gay - ha ha ha!" laughs one. "He's got no money either, has he? He has to con it all off his mam. He's greedy and he doesn't think about anyone other than himself."

Dean Hanson, 11, tugs at my sleeve: "They're all parasites, all of them," he says, his big eyes under the peak of his baseball cap. "They're greedy too. What a pig. He should get 50p a year and work like everybody else. She's better than him; she does more than what he does. He's a lazy toerag."

Joy Taylor, 64, and her daughters Maureen Templeton, 42, and Janet McAdam, 41, are more confused. "They should work for a living like everyone else; he should work like we have to." "He should spend some time with ordinary people; he's supposed to be working for us..."

"No he's not; he works for his mam."

"Well, he should spend more time in North Shields doing what we do."

"I think he's a good man, but he should get out and see the public a bit more. He's definitely not up here enough."

"She's had a bit of a blow with the baby, but she's not alone; that happens to a lot of people. As for the work, he was chasing a dream, wasn't he? I don't suppose there's anything wrong with that."

For those who meet the couple inside the YMCA, however, the royal charm still works. Vix - she doesn't want her full name used - a teacher accompanying some first-aiders, is deeply sceptical about the couple prior to the visit, but after 10 minutes with the countess she is flushed and beaming. "I'm embarrassed... I'm genuinely surprised at how nice they were. They were not as posh as I thought they would be and they seemed interested in what we were doing," she babbles.

Across Newcastle that evening and in Manchester last night, husbands, mothers, children and publicans will have heard stories about the day the couple came to visit. Royal approval still means something to voluntary organisations, charities, schools and those in the arts whose work goes largely unrecognised. Here, at least, the family still has a role; whether the Wessexes can fill it remains to be seen.