The OFT, which has intervened before on issues such as the sale of payment protection insurance, has wide-ranging powers to restructure the market and make firms sign up to binding agreements in cases where this is felt necessary.
The investigation comes at a time when MPs have been looking at how to tackle spurious whiplash claims, which have also been ramping up premiums.
Prime Minister David Cameron has vowed to take on the “compensation culture”, including the £2bn-a-year costs associated with whiplash.
Proposals include consulting on the feasibility of introducing independent medical panels.
The independent medical experts, who would have no direct links to either claimants or defendants, would replace the current assessment of whiplash injuries by either GPs or doctors.
The cost of third-party property damage to the private motor insurance market in the UK, including repairs, is about £1.4bn .
Under the law, drivers who are not at fault are entitled to be put back in the position they were before the accident happened, which could include receiving a replacement vehicle.
The OFT found that insurers of the driver at fault had “little control” over how repairs and courtesy car services were carried out.
The watchdog highlighted further practices including agreements between insurers and repairers to charge higher labour rates.