The aircraft on the radar screen become visible only in the final few seconds of descent, as they break through the dense grey cloud hanging over west London. Looking down from Heathrow's 85-metre (280ft) control tower, the wider issues that Britain's busiest airport has been grappling with are far easier to make out.

To the south, the perfectly arranged rows of aeroplanes parked at the gates of the gleaming Terminal 5. To the north, the bizarre geometry, cul-de-sacs and weary grey blocks of the central airport hub. To either side, hulking A380s dwarfing the jets of the past as they taxi their vast wingspans down narrow lanes. Beyond, the village of Sipson, in the place where the airport's owners, BAA, dearly wanted one end of a third runway to be.

Officially, the debate about Heathrow expansion is dead and buried, with the environmental case having gained conclusive, cross-party backing.

Yet many within the aviation industry still regard it as the only feasible, medium-term solution for airline capacity in Britain. On Tuesday, London First – a lobbying group representing many of the capital's biggest businesses – said the government was "negligent" and "irresponsible" to rule out a bigger Heathrow. Its commission's report set out in uncomfortably blunt terms what many in aviation, business and politics privately say: that the Conservative party foolishly painted itself into a corner in opposition by declaring outright opposition to Labour's plans for a third runway.

Now in government, it has a transport secretary in Justine Greening who campaigned hard in 2009 as a Putney MP to prevent any addition to the flight path over her constituency. The public common cause made with environmental groups seems to some in the Conservative party as dated as Cameron's pledge to make his the greenest government ever: a political anachronism in a time of negative growth and economic crisis, when jobs and stimulus are drowning out other concerns.

Weeks after Labour under Ed Miliband declared the environmental impact meant it no longer backed a third runway, the chancellor, George Osborne, took the unusual step in his autumn statement of pledging to look at all the options for "maintaining the UK's aviation hub status". However much his ear was bent by the business groups demanding the possibility of daily direct flights to the emerging markets of China and elsewhere in Asia, Heathrow expansion was again explicitly ruled out.

This spring, the government will set out its plans for aviation. With new runways at Gatwick or Stansted also ruled out, if more capacity is needed – and both the Tories and Labour appear to believe this is the case – the only remaining option appears to be a new airport. Yet for all that London's mayor, Boris Johnson, insists his futuristic vision for British air travel is realistic, the prospect of a "Boris island" airport in the Thames estuary – several times mooted and forgotten in the past – seems, at the very least, decades away.

In the Heathrow boardroom, with its panoramic views from the ageing jumble of concrete in the east across to the three neat glass buildings of Terminal 5, BAA's chief executive, Colin Matthews, is relaxed about Thames estuary plans, which have allowed him to air arguments he believes are little understood.

There is a fundamental difference, he says, between simple airport capacity and hub capacity. Only the latter can make certain long-haul schedules feasible, by providing sufficient numbers of transfer passengers to fill a daily direct flight to Hyderabad, as British Airways does now, or to future destinations such as Guangzhou in markets that British business is eyeing hungrily.

Stansted and Gatwick could easily take more passengers, but neither are hubs. While Johnson recently described Heathrow as being "fundamentally in the wrong place", Matthews points out that the M4 corridor is congested for a reason: that businesses have located to be near the airport, not vice versa. None of the solutions for hub expansion are easy, Matthews says, but "it would be irrational to rule out the obvious one".

Francis Salway, the outgoing boss of Land Securities and a member of the London First commission, said: "People have talked very little about the cost of providing the new transport connections, homes, services and schools for a workforce that would presumably shift from the Heathrow area to somewhere in the Thames estuary. It would be irresponsible to not even consider Heathrow expansion as an option."

Heathrow remains the world's third largest airport. Last year it handled 476,197 flights, 99.2% of the limit permitted by the Civil Aviation Authority. Operating so close to capacity makes the airport vulnerable to disruption. Rules on alternating take-off and landing, and changing flight paths to preserve local residents' sanity, mean controllers can't use the slots as efficiently as they might: planes from Terminal 4 sometimes have to taxi right across the south runway, taking a potential slot away.

While one obvious solution seems to be bigger planes, the turbulence created by A380s means the following takeoff has to be delayed another minute for safety. And the skies around are also congested: according to NATS, the air traffic control service, the lack of sufficient runway capacity to meet demand only crams the airspace further, with planes needing to be placed in holding patterns before they can land.

While Willie Walsh, chief executive of British Airways' parent company, IAG, has declared bullishly that the national airline, which uses roughly half of Heathrow's capacity, is not moving to "Boris island", others mutter darkly about IAG one day relocating to Madrid if Heathrow can't become the super hub of the future.

According to Walsh: "Heathrow has hugely improved, compared even with five years ago. Terminal 5 has transformed BA's operations and Heathrow is a global brand – you can go anywhere in the world and people have heard of it.

"The problem is that the government lacks ambition. In isolation, the cancellation of the third runway might not be a major problem, but the government has failed to identify any tangible alternative to address the critical national issue of runway capacity."

All this, of course, ignores the wider backdrop of a nation pledged to cut carbon emissions and the aviation industry's ever-larger footprint. Yet the local politics that originally did for expansion might swing around if the lobbyists successfully make the case that Heathrow's long-term future is in doubt, along with thousands of jobs – 76,000 at the airport itself.

London First's call is unlikely to get Heathrow expansion back on the Westminster agenda any time soon. But it shows this is an issue that business lobbyists have not forgotten – and that in future years, climate campaigners may have to fight the third runway battle all over again.