Drivers are facing fresh upward pressure on their car insurance premiums following sharp increases to insurers' own costs.

Brokers have put the rising costs down to increasing concerns by reinsurers over the way in which people are being compensated for accidents.

Reinsurers offer "insurance for insurers", by taking on the risks of the insurance firm which has a direct contract with the customer.

Broker Willis Re said UK motor insurers which had big enough losses to trigger reinsurance payouts saw rate increases of 35% and upwards on policies which took effect from January. Those which did not rely on reinsurance payments faced rises of 20%-30%.

The Financial Times reported that the knock-on effect for UK policyholders could be a 3%-10% premium rise, according to some estimates, which would mean hundreds of pounds extra for some drivers.

Willis Re said that larger, more serious bodily injury claims are increasingly being settled by periodic payment orders (PPOs), which are paid at regular intervals over the lifetime of someone who has been injured, rather than a one-off sum.

Grange Turner, executive director of Willis Re, said this has created greater uncertainty for insurers and reinsurers, which need to weigh up factors such as the life expectancy of a claimant and wage inflation.

He said: "Many reinsurers have become increasingly concerned about taking all of these variables on to their own balance sheets."

The added cost pressures come at a time when young female drivers in particular are already predicted to see their car insurance premiums shoot up, after European rules came into force last month banning insurers from taking someone's gender into account when calculating how much their insurance should cost.

Young women are forecast to be among the worst affected due to the comparatively high accident rates of young men.

Peter Harrison, car insurance spokesman for comparison website MoneySupermarket, said: "Any additional cost won't go down well and I'm sure that cost will be passed on."

Mr Harrison said the competitive nature of the market kept premiums on a downward slide over the last year.

But he said that any price adjustments as a result of the new gender rules are likely to become clearer in the next few weeks.

"We will see a lot of volatility in the next few weeks," he said. "This has been a very big change in the way that people do things."