A typical motoring premium for a young adult could increase from around £2,400 a year to £3,600, warned accountancy firm Mazars.
The expected rises could make motoring unaffordable for many, particularly badly affecting those living in rural areas, the company said.
It added that the hike in premiums could lead to more young people driving uninsured or giving false information to reduce the cost of insurance.
Some young motorists might also switch to motorcycles where the fatality rate is much higher than in cars.
Mazars added that more young people would be tempted to live in metropolitan areas and that parents' "taxi services" for their offspring could extend from younger children to older ones.
Craig Scarr, an insurance industry partner at Mazars, said: "While public transport is plentiful in metropolitan areas, the car is often essential for getting to work in rural and many suburban areas.
"We are already seeing younger adults are being priced out of car ownership and cannot afford it, and this will hit even harder over the next year as a typical premium for a young adult rises from £2,400 currently to over £3,600."
"The insurance industry needs to look at innovative ways to allow young drivers to get affordable insurance, while penalising boy-racers."