The £9.4 billion car insurance market has been referred to the Competition Commission by the Office of Fair Trading because of concerns the structure of the market was making costs and premiums unnecessarily high.
Premiums, it said, were being pushed up by £225 million a year - £10 per policy.
It also found that insurers of at-fault drivers had no control over the amount spent on repairs or replacement vehicles by not-at-fault drivers.
The Commission has up to two years to report its findings.
The OFT said in May the market needed more investigation. It has reached its final decision after public consultation.
"Competition appears not to be working effectively in the private motor insurance market," said OFT chief executive Clive Maxwell.
"The insurers of at-fault drivers appear to have little control over the bills they must pay, and this may be leading to higher costs for them and ultimately higher premiums for motorists."
The OFT was particularly concerned that replacement vehicles being provided could be unnecessarily expensive and they could be being provided for longer than necessary.
The regulator's report earlier in the year suggested that the market was "dysfunctional".
It said after crashes, many insurers of not-at-fault drivers, brokers and repairers, refer the drivers to organisations that tend to charge higher rates in exchange for referral fees of around £250 to £400 per hire car.
The bills paid by the insurers of at-fault drivers can be inflated further because not-at-fault drivers are given replacement vehicles for longer than necessary.
When it comes to repairs, bills paid by the insurers of at-fault drivers are pushed up because some insurers receive referral fees and rebates from repairers and suppliers.
And some insurers even have agreements with repairers to charge higher labour rates when repairing the vehicle of the not-at-fault driver.
These practices boost the revenues of the insurer of the not-at-fault driver as well as pushing up the costs for the insurers of the at-fault driver.
The higher costs are eventually passed on to drivers through higher premiums.
The report said that such practices were pushing up total premiums by about £225m a year.
The Association of British Insurers (ABI) welcomed the review.
"The OFT found what insurers have known for years - that when a customer has a crash that is their fault, their insurer has little control over the cost of the subsequent claim," said Nick Starling, the ABI's director of general insurance.
"Regulation of all players in the market to tackle excessive costs is needed, and we look forward to working with the Competition Commission to bring much needed reforms to the market that will, in turn, result in lower car insurance premiums for everyone."
However, the Credit Hire Organisation (CHO), which represents car hirers, said premiums were rising owing to an increase of whiplash claims ahead of anything else.
Martin Andrews, chief executive of the organisation, argued that giving at-fault drivers' insurers more control could mean they try to avoid ways of giving the not-at-fault driver a replacement car.
"We continue to have serious concerns as to the long-term impact it may have on the motoring consumer and their right to mobility after an accident that was not their fault," he said.