Car registrations plunged in March, according to figures from industry body the Society of Motor Manufacturers and Traders (SMMT).
Preliminary data shows the UK new car market shrank by 15.7% last month compared with 2017.
Demand for diesel vehicles fell 37%, but demand for petrol was flat and that for alternative fuel models rose 5.7%.
March 2017 was a record month as customers bought new vehicles ahead of a change in Vehicle Excise Duty.
New car sales fell for the first time in six years in 2017, with a 5.7% decrease to about 2.5 million vehicles.
Demand for diesel cars plunged by 17% last year, meaning the pace of decline for such vehicles in March has more than doubled.
Analysis: Theo Leggett, BBC business correspondent
At first glance, this looks like deeply worrying news for the automotive industry. But it it's worth remembering that in March 2017, new car registrations hit a record high. Buyers were rushing to get hold of new vehicles ahead of big changes to the vehicle excise duty regime, which sharply increased the rates payable on some cars.
But we can say with certainty that registrations have now been falling steadily for a whole calendar year. The SMMT has consistently blamed economic uncertainty, which it links to Brexit and the collapse in diesel sales.
The latest figures show that the move away from diesel seems to have accelerated. That suggests that the industry's attempts to convince consumers and politicians that modern diesels are clean and have a future are failing badly.
By historical standards, new car registrations are still at pretty high levels. The steep fall in March might be a glitch. However, the overall trend cannot be ignored - and that is what the industry will be worried about.
Mike Hawes, SMMT chief executive, said: "March's decline is not unexpected, given the huge surge in registrations in the same month last year.
"Despite this, the market itself is relatively high with the underlying factors in terms of consumer choice, finance availability and cost of ownership all highly competitive.
"Consumer and business confidence, however, has taken a knock in recent months and a thriving new car market is essential to the overall health of our economy."