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Comprehensive motor insurance premiums fell by £36, or 8.9%, on average in 2013, according to insurers.

The average annual policy, bought during the final three months of the year, cost £370 compared with £406 a year earlier, the Association of British Insurers (ABI) said.

Insurers' predictions of falling claims for whiplash has helped lower prices.

However, the cost rose by £5, or 1.4% in the final quarter of the year compared with the previous three months.

The figures are based on data recording the amount people pay when actually taking out or renewing policies, rather than quoted prices, but only covers comprehensive policies - the most popular type of insurance among drivers.

ABI research also showed that eight in 10 people buying motor insurance spent time comparing prices before buying.

A change in the civil legal system had helped to push down prices, but the ABI said that more could be done to tackle fraudulent claims which would reduce prices further.

In December, the Competition Commission - which had been studying the £11bn private motor insurance industry - said that the cost was "unnecessarily high" for all drivers owing to the complex chain of claims.

The higher premiums came from the cost of courtesy cars and repairs, which is paid by the insurers of motorists who caused the accident.

The Commission discovered that post-accident repairs were often shoddy. It is now considering ways to fix the market, with a final report due to be published by September 2014.

The options include a cap on the cost of replacement vehicles, or making an insurer of the not-at-fault driver responsible for providing the replacement vehicle. Alternatively, the insurer of the at-fault driver could manage the claim.