But across the motor insurance market generally, competition appears to be slackening off, Comparethemarket.com found - which could pave the way for further price hikes for motorists in other age groups.
Across all age groups, the price difference between the average policy on offer and the cheapest they could get if they shopped around is at its widest levels in 2015 so far - reaching nearly £100.
The Premium Drivers report from the website is based on actual quotes that people have received and it includes both comprehensive and third party cover.
It found that the gap between the average premium that drivers aged under 25 are being offered and the cheapest they can get on the market is narrowing - suggesting that competition is heating up in this area of the market.
The difference for under-25s between the average premium on offer and the cheapest has decreased from 21.2 per cent in August 2014 to 19.2 per cent in August 2015.
The average premium being offered to a driver aged under 25 is now £1,154.54, while the cheapest quote for this age group is £924.59, the website said.
Simon McCulloch, director of insurance at Comparethemarket.com, said: “If price competition continues to be high for young drivers’ policies, we may in fact see premiums start to decline for under-25s whilst they rise for everyone else.
“This will particularly be the case if telematics policies continue their rise in popularity and price competitiveness.”
Telematics, or “black box”, insurance policies work by tracking a vehicle’s movements, helping insurers to reward good drivers with cheaper premiums.
Comparethemarket.com found that more than three-quarters (77 per cent) of under-25s are seeing at least one telematics premium crop up in their cheapest five quotes - up from 62 per cent in 2014.
It said signs that telematics policies are becoming increasingly commonplace and competitively priced are helping to drive up competition between insurers for customers in the under-25 age group.
Among all age groups, Comparethemarket.com found that the average cheapest policy costs £517.73 - which is a £75 increase compared with a year ago.
There is also a £97.95 difference between this and the average premium on offer, at £615.68.
The report said that in general, drivers can expect to see hikes in the cost of car insurance in thecoming months, amid continued high levels of personal injury claims that add to the cost of everyone’s policies.
Insurers have also warned that millions of customers will face higher costs for cover after a hike in taxes charged on insurance products.
Chancellor George Osborne’s summer Budget revealed that insurance premium tax will be increased from 6 per cent to 9.5 per cent from November.
Mr McCulloch said that in the current tough market conditions, insurers are even more likely to steadily raise the cost of people’s renewal quotes.
He said: “The reality is that, on average, automatically renewing your car insurance will cost you about £100 extra - a cost that few people would be happy to bear.”