Chief executives from some of the UK’s biggest insurers will meet the prime minister on Tuesday to debate what needs to be done to tackle the “whiplash epidemic” pushing up the cost of motor insurance.

The Association of British Insurance’s director general, Otto Thoresen, will be joined at the summit with David Cameron by the bosses of Admiral, AXA, Aviva, Co-operative Financial Services, RBS Insurance and Zurich. Whiplash claims are costing insurers £2bn a year and adds an extra £90 to the average motor insurance premium, the ABI says. Over the last three years, the number of people claiming whiplash has jumped by 32% to 570,000 a year, even though the number of accidents reported has fallen by 16% to less than 210,000.

The industry body will urge the government to introduce legislation to crack down on the UK’s whiplash epidemic, which now sees a whiplash claim being made every minute. This could include introducing a minimum speed under which any whiplash claim could be rebutted, as in other European countries, and a court-appointed pool of impartial medical experts including specialists in whiplash diagnosis.

The ABI is also proposing a reduction in fixed legal fees as part of the ban on referral fees. Lawyers and solicitors have been banned from receiving referral fees but in road accidents customer details are also sold by garages, car hire firms and even ambulances and the police to personal injury lawyers and claims management firms. Former justice secretary Jack Straw has lambasted this practice as a “dirty secret” and a “racket”.

Thoresen believes the summit is a “unique opportunity to highlight to the prime minister the unacceptable cost pressures that insurers are facing, and what needs to be done to ensure that the UK’s honest motorists get a better deal”. He added: “We welcome the personal interest of the prime minster in this and the government’s willingness to consider radical reforms which will be necessary to tackle the UK’s compensation culture.”

To improve the road safety of young drivers and bring down their soaring motor insurance costs, the summit will discuss the introduction of a minimum pre-test learning period, a structured learning programme, graduated licensing and a zero alcohol limit for young motorists.

Last week the AA launched its first black box insurance product, which uses telematics to track the driver’s performance, on which premium adjustments are made, and is aimed at young and inexperienced drivers.

The Co-operative was the first major insurer to launch a black box insurance policy for young motorists last March and will tell Cameron drivers with a box are less likely to be involved in a car crash, and the accidents they do have are less serious, leading to a 34% reduction in the cost of accidents.

“The cost of insurance has hit an all-time high, especially for young drivers who feel that they are being priced off the road,” said the Co-op’s director of general insurance David Neave. “It would be great to see more insurers follow suit and offer similar schemes.”

Around 90% of young drivers have seen hundreds of pounds shaved off their premiums in exchange for sticking to speed limits, braking and cornering carefully and limiting night-time driving. The insurer estimates that £20m will be given back to customers in discounts for good driving over the next three years.

According to the AA, the ‘shoparound’ price for annual comprehensive cover rose by £130 to £971 in January from 12 months ago. The north-west has the highest average premiums at £1,615, followed by London at £1,120. The AA measures premiums quoted. Data from the ABI shows premiums paid rose by 12% between 2009 and 2010 and a further 9% in the first three quarters of 2011.