Data from the Society for Motor Manufacturers and Traders (SMMT) show a drop of 44.4% compared with last year.
March is usually one of the strongest months of the year for the car industry.
But the Covid-19 outbreak has taken a heavy toll, forcing potential customers to stay at home for the past fortnight.
New number plate registrations are released in March and September every year.
But last month new registrations dropped by about 200,000 compared with the same period last year.
They fell to the lowest level in March for more than two decades.
The crisis has come at a difficult time for the motor industry, which was already suffering with falling sales and a collapse in demand for diesel vehicles, while struggling to meet tough new emissions targets.
The coronavirus outbreak has also halted car production.
All of the UK's major car factories suspended work last month, and it is not yet clear when they will reopen.
In total, 254,684 new cars were registered in March according to the SMMT, a fall of 203,370 compared with March 2019.
Demand from private buyers and larger fleets fell by 40.4% and 47.4% respectively.
At the same time, the numbers of petrol and diesel cars reaching the country's roads were down 49.9% and 61.9% respectively.
However, registrations of battery electric vehicles rose almost threefold to 11,694 units, accounting for 4.6% of the market, while plug-in hybrids grew by 38%. Hybrid electric vehicles fell 7.1%.
The SMMT said it now expected car sales of 1.73 million in 2020, 25% lower than last year.
Larger falls in new car registrations have been reported in other European countries, with Italy down -85%, France -72% and Spain down -69% in March, the SMMT said.
SMMT chief executive Mike Hawes said, "With the country locked down in crisis mode for a large part of March, this decline will come as no surprise.
"Despite this being the lowest March since we moved to the bi-annual plate change system, it could have been worse, had the significant advanced orders placed for the new 20 plate not been delivered in the early part of the month.
"We should not, however, draw long-term conclusions from these figures, other than this being a stark realisation of what happens when economies grind to a halt."
Mr Hawes added that it was uncertain how long the market would remain stalled, but it would reopen and the products would be there.