Motorists are seeing the cost of taking out car insurance increase for the first time in more than two years as efforts to clamp down on fraudulent claims have not delivered the savings that insurers had anticipated, according to a report.

The typical quote for someone who shops around for an annual comprehensive policy edged up by £6 or 1.2% over the three months to September 30, to reach £531 on average, according to an index run by AA Insurance, which compiles the average of the five cheapest quotes on the market.

This marks the first quarterly increase in the cost of motor insurance since spring 2012, although the average premium for someone who shops around is still 14.4% or £89 cheaper than a year ago.

Janet Connor, managing director of AA Insurance, said some opportunities to stem the tide of fraud have been "missed", and car insurance premiums are therefore likely to creep up further in the coming months.

Looking at the motor insurance market as a whole and not just the cheapest deals, quotes for annual cover generally have increased sharply by 4.2% to reach £891 on average.

This shows that it is becoming even more important for consumers to shop around for a motor insurance deal and suggests that while there is still strong competition among the cheapest car insurance providers, cost pressures on insurers for claims such as whiplash are generally pushing premiums upwards, the report said.

Ms Connor said that insurers had reduced their prices in anticipation that a Government clampdown on fraudulent and exaggerated personal injury claims would have an impact on the costs that they were having to bear. Whiplash claims are estimated to add around £90 to the typical cost of a car insurance policy.

Ms Connor said: "But the truth is, falling premiums had more to do with competitive tension than any benefit afforded by reforms.

"Premiums are, on average, now similar to their 2010 level and are no longer economically sustainable."

She added: "My view is that many opportunities have been missed. As a result, I believe that this small upward move in premiums will lead to further modest increases over the coming months."

Wales is the only area in Britain where motor insurance premiums for people who shop around have continued to edge down in recent months, falling by just over £1 on the previous quarter to reach around £475.

The biggest recent increases in car insurance costs have been recorded in southern England, which has seen the average cost of comprehensive cover jump by around £9 over the last three months to reach £455.

Scotland remains the cheapest place to insure a car, with the typical cost sitting at £380, which is around £3 more expensive than three months earlier.

North-west England is still the most expensive region to insure a car, with the average cost of an annual policy at £786, which is around £6 more expensive than the previous quarter.

Changes which have been previously unveiled by the Government to tackle the "compensation culture" and crack down on bogus and exaggerated claims include establishing greater independence for experts who produce medical reports for personal injury claims as well as reforms to ''no win no fee'' deals.

Lawyers can no longer double their fees if they win, at the expense of defendants and their insurers. ''Referral fees'' paid between lawyers, insurers, claims firms and others for profitable claims have also been banned.

There have also been recent signs of stronger action to break up criminal gangs who take part in scams such as ''crash for cash'', when a driver deliberately slams on their brakes so that the unsuspecting motorist behind hits them.

But the AA said many insurers are still reporting surges in the number of lower value crash for cash claims, suggesting that the number of opportunistic attempts at such claims is growing.