The amount motor insurers pay out in claims looks set to jump from £8.5 billion in 2007 to £10.9 billion by 2012, according to market analyst Datamonitor.
The main factor diving the rise is the increased cost of personal injury claims arising from road traffic accidents.
The group said that although improvements in road safety had reduced the number of accidents there were each year, insurers were still seeing their payouts rise due to increases in medical and legal costs.
Between 2002 and 2006, the total number of road accidents fell from 222,000 to 189,000, but at the same time the average payout to somebody who was injured in an accident rose from £4,277 to £5,331 during the same period.
As a result, total claims costs rose from £7.1 billion in 2002 to £8 billion in 2006.
Author of the report Mahreen Hussein said: "Personal injury claims continue to constitute the largest bill for motor insurers.
"Strong rates of inflation relating to medical costs and legal costs are the primary reason behind escalating bodily injury costs which have grown significantly in recent years."
At the same time, the cost of repairing a vehicle has also increased, with both garage repair bills and the cost of replacement parts rising.
A spokesman for the Association of British Insurers said: "In recent years claims costs have been rising for insurers, and one of the key factors has been rising personal injury costs."
But he said insurers had no idea what was going to happen to these costs in the future.
He said: "Insurance companies are looking at ways to keep claims costs under control and premiums under control."
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