The Competition and Markets Authority (CMA) is proposing to cap the cost of providing a courtesy car following an accident after finding there is often "little or no incentive" to keep expenses down.
Replacement vehicles collectively cost consumers between £70 million and £180m a year through higher premiums, the CMA found.
AA Insurance estimates that if the CMA's recommendations are implemented they could wipe about £20 off the cost of the average motor insurance premium.
Premiums have already been tumbling in recent months amid wider Government moves to weed out bogus personal injury claims that have ramped up the cost of motor insurance generally.
According to an index run by AA Insurance, the average quoted premium for someone who shops around has already fallen by more than £100 over the last 12 months, to £531.
The CMA is also proposing that competition in the £11 billion private motor insurance market should be boosted by banning "price parity" agreements between comparison websites and insurers, which block insurers from making their products available to consumers more cheaply elsewhere.
It said consumers should also be given clearer information about their rights following a motor accident and better explanations about the costs and benefits of taking out protection against their no-claims bonus.
The CMA also recommends that City regulator the Financial Conduct Authority looks at how insurers communicate with consumers about add-on products related to motor insurance.
The cost of providing a courtesy car can be inflated after an accident because often, while it is the insurer of the innocent party in a car accident that arranges for their car to be temporarily replaced and repaired, it is the insurer of the driver deemed to have caused the accident that picks up the tab.
This divide between who organises the courtesy car and who pays for it results in a lack of incentives to keep costs down.
Although the inflated cost is initially felt by the insurer of the driver who is at fault, it eventually feeds into everyone's premiums.
The CMA, which superseded the Competition Commission earlier this year, will consult on the plans before publishing a final decision in September.
The proposals received broad backing from insurers - and from brokers, who are hopeful the moves will help them to offer cheaper insurance deals than those appearing on comparison websites.
James Dalton, head of motor insurance at the Association of British Insurers, said the moves would help reduce the "often inflated bills" from credit hire operators and should help lower premiums.