Car insurance premiums could increase by an average of £60 a year, following changes to the formula for calculating injury compensation payments.
The insurance industry has called it a "crazy decision" by the Ministry of Justice.
The move - reducing the so-called discount rate - could also cost the Department of Health £1bn.
When the victim of an accident is awarded compensation in a lump sum, the discount rate reduces their payout.
This is is to make up for the extra money they make by investing that lump sum over many years.
The Ministry of Justice has decided to reduce the discount rate from 2.5%, to minus 0.75%.
This is because the formula is based on gilt yields, or the interest rate on government bonds.
By the time inflation is taken into account, real returns on such bonds have become negative.
Reducing the discount rate to minus 0.75% was a "crazy decision", said Huw Evans, Association of British Insurers (ABI) director-general.
"Claims costs will soar, making it inevitable that there will be an increase in motor and liability premiums for millions of drivers and businesses across the UK. We estimate that up to 36 million individual and business motor insurance policies could be affected in order to over-compensate a few thousand claimants a year," he said.
Experts said the formula change could put £60 on the average car premium, and cost younger drivers as much as £107 a year.
Where personal injury claims are made against the NHS, the bill could rise by £1bn, the Treasury said.
However, the government is to launch a consultation on how the system can be made fairer.
In the meantime it has made it clear it had no choice but to change the discount rate, according to the existing law.