Failures in the "dysfunctional" car insurance market have "encouraged criminality" in some areas, according to the head of a parliamentary transport committee.
Louise Ellman, Labour MP for Liverpool Riverside, said: "This is our fourth report on the cost of motor insurance and while premiums are now falling, aspects of the market remain dysfunctional and have encouraged criminality to take root.
She said further action was needed to tackle fraud which the report said is pushing up insurance prices for motorists.
The youngest drivers, who pay most for comprehensive insurance, enjoyed the biggest dips in premiums in the first part of this year, with the cost for 17 to 22-year-olds coming down 20.5% compared with the first three months of last year and 23 to 29-year-olds getting a 19.9% fall.
Regionally, the north west of England saw the biggest dip - of 20.9% in premiums at the beginning of this year, while Anglia had the smallest decrease - 13.3%. However, the AA warned that this could be the end of the good news for motorists.
AA Insurance director Simon Douglas said: "Legal reforms introduced by the Justice Ministry to curb organised attempts at whiplash injury fraud coupled with better fraud detection by insurers have also certainly helped put downward pressure on premiums."
The AA has said that car insurance premiums have fallen sharply, with the average price dipping more than £100. For the first three months of 2014, the average comprehensive motor insurance "shoparound" figure, involving quotes from a number of markets, had plunged to £531.
This was 5.6% down on the figure for the last three months of 2013 and 16.6% down on the January-March 2013 figure.
The January-March 2014 figure for third party, fire and theft was £725 - an 8.4% drop on the last three months of last year and 18.5% down on the figure for the first three months of 2013.
The Competition Commission claimed that in most cases the party managing the accident claim - typically the non-fault insurer or intermediary - was not the party liable to pay the costs of the claim.
The commission estimates the extra premium costs due to the separation of control and liability on replacement cars and repairs to be between £150 million and £200 million a year.
It is considering whether to make a driver's own insurer responsible for providing a replacement vehicle or to give at-fault insurers greater opportunity to take control over managing claims.
There may also be caps on the cost of providing a replacement vehicle and on repair costs, as well as compulsory audits of repair quality after the watchdog found that following an accident too many repairs were not completed to the required standard.