Parents of young female drivers take note: a little black box could save you hundreds of pounds on car insurance for your daughter. But for the biggest benefit, you need to act fast. From next Friday an EU ruling will ban insurers from discriminating between men and women, meaning that women drivers end up spending more on their car insurance.

One insurer, insurethebox.com, estimates that the change could cost women an extra £500 a year on average. This will be particularly noticeable for young female drivers between 17 and 22, who already pay a typical £2,057 a year for cover according to the AA.

Pundits claim that buying a telematics (sometimes known as a "black box") policy could be the best way for female drivers to keep their premiums down. These record how a car is driven and let insurers tailor the cost of cover so that drivers who prove themselves to be responsible end up paying less; such policies typically save careful young drivers around 25% to 30% off their premium.

Telematics policies are now offered by more than a dozen insurers and fall into three categories: curfew-based policies that offer a discount if you do not drive between 11pm and 5am; policies that discount for low mileage; and behaviour-based policies that take into account things such as cornering, braking and speeding. The third type of policy is the most common. Drive consistently well and your premium comes down over time; drive badly and you are penalised.

"The whole point of these policies is that drivers can take control of their insurance costs," says Graeme Trudgill of the British Insurance Brokers Association (Biba). "Based on results from the black box, insurance companies charge an annual premium correlating to that risk over the year. Behaviour-based policies are the best telematics policies as they genuinely reflect your driving."

Telematics insurance is relatively niche but is taking off. Figures from Biba show that black box motor insurance sales have increased five-fold in the last two years, from 35,000 policies in 2010 to 180,000 in the first half of this year. The number, predicts Biba, will reach around 500,000 in the next 18 months.

However, one factor putting off a lot of young drivers is the fear that "big brother is watching". Who will own and have access to the data – and under what circumstances it will be shared?

"At the moment the data is not shared, it is owned by us, the client and the insurer," says Lisa McPherson, chief executive of Autosaint, a broker that sells black box policies on behalf of two different insurers.

However, while details of your driving habits may not end up in the hands of the authorities, Trudgill says the industry is discussing the protocol for sharing "incident data" (ie, if you have a car crash) with the police. And parents may well be able to take a look at their child's every move. "We are not ashamed of that," says McPherson. "Around 70% of parents are paying for their teenager's insurance and these policies are about getting those parents involved and encouraging their children to drive more safely."

If the figures are to be believed, the results are striking. Insurethebox, for example, claims that its incentives for safe driving have reduced accidents among 17- to 21-year-olds by 35-40%. The Co-operative says it has seen car crashes drop by a fifth among users.

The discount is taken off a base premium calculated at the outset of the policy, and for young female drivers this base premium will rise with many insurers from Friday. So if you are considering this option, get in quick. An added bonus is that as long as you conclude the contract before 21 December, you can often start your policy for 30 days after that date and not be affected by gender neutrality rules.

Insurers offering telematics policies include the Co-op, Swinton, Autosaint, Admiral, Coverbox and Insurethebox. Aviva recently became the first insurer to offer a policy that monitors driver behaviour via an app, Aviva Drive, that can be installed on a mobile phone and this type of policy is likely to become more commonplace.

But lack of standardised data makes the different offerings hard to compare. As a general starting point, those who regularly drive at night – perhaps students undertaking bar work – will find that many of the policies are unsuitable as drivers are penalised for taking the car out after 11pm. The same applies to those who may regularly drive badly, especially if exceeding the speed limit.

Insurers make various claims as to the typical premium charged. Autosaint says it is £1,800, while the Co-op claims its average premium, before a driver behaviour discount, is £1,300. Even this does not offer a meaningful comparison, however, as some policies work by offering the bulk of any discount up front. Others will charge a higher premium to start with and offer a larger discount later, depending on driving behaviour.

The Co-op, for instance, factors a 25% discount into that initial typical £1,300 premium and offers a further cut of up to 10% in a year's time depending on driver behaviour. "We work on the basis that if someone wants one of these policies they are probably already a more responsible driver, which is reflected in the upfront discount," a spokeswoman said.

From next weekend, the Co-op is offering a double discount (20%) on driver behaviour for a limited period. This may not be as good as it sounds however, as the Co-op is one of the insurers yet to confirm its price increases for female drivers. The extra 10% discount may simply work to negate some or all of an increased premium from Friday.

Nevertheless, Joanne Garcier, head of telematics at price comparison website Confused.com, says she would favour upfront discount policies: "The choice is ultimately down to how confident a driver is in their own driving behaviour, but I think most drivers would be happier knowing they are getting the bulk of their discount upfront, regardless of how they then drive."

Trudgill says that drivers need to look carefully at how the policies work before making a decision: "People do need to know what it is that is going to be mainly affecting their premiums. Where do the penalties start or stop? Drivers need to look for insurers which make that very clear at the outset of the policy."