Industry bosses said news of a 3.4 per cent year-on-year decline in UK-wide registrations was of “clear concern”.
Some 458,000 new cars were registered last month across the UK compared with 474,000 during March 2018, the Society of Motor Manufacturers and Traders (SMMT) said.
Private and business registrations fell by 2.8 per cent and 44.8 per cent respectively during the month, while fleet sales rose by 0.3 per cent.
Sales of petrol models increased by 5.1 per cent year-on-year last month, while diesels slumped 21.4 per cent.
Demand for alternatively fuelled vehicles (AFVs) such as hybrids and pure electrics increased by 7.6 per cent to take a market share of 5.5 per cent.
In Scotland, it has emerged that the new car market declined by 9.4 per cent, year-on-year, last month.
March is a crucial month for the industry, as the number plate change – this year to 19-plates – traditionally brings buyers into showrooms.
SMMT chief executive Mike Hawes said: “March is a key barometer for the new car market, so this fall is of clear concern.
“While manufacturers continue to invest in exciting models and cutting-edge tech, for the UK to reap the full benefits of these advances we need a strong market that encourages the adoption of new technology.
“That means supportive policies, not least on vehicle taxation and incentives, to give buyers the confidence to invest in the new car that best meets their driving needs.
“Above all, we urgently need an end to the political and economic uncertainty by removing permanently the threat of a no-deal Brexit and agreeing a future relationship that avoids any additional friction that would increase costs and hence prices.”
Sandy Burgess, chief executive at the Scottish Motor Trade Association, said: “There can be no doubt that this softening of the market recorded in business registrations has been fuelled in some part by continued political uncertainty.
“We continue to operate this roller coaster ride with the consumers’ confidence levels under attack from the backlash of uncertainty caused by Brexit.
“Despite the challenges affecting the sector our members continue to demonstrate their adaptability and resilience capitalising on the opportunities provided by other business areas including used cars, aftersales and the rise of the alternative fuel vehicles.”
Mat Watson, resident motoring expert at www.carwow.co.uk, said: “March is usually a peak month for new car registrations, with the biannual plate changes that only happen in March and September driving a flurry of brand new car purchases.
“This 3.4 per cent decline, and the specific 2.8 per cent drop in private sales is a stark demonstration of how Brexit has created uncertainty in the motoring space.
“Whilst this is a weak March on paper, there is absolutely no doubt that this could have been a lot worse; a combination of buyers keen to lock down their wheels before Brexit and the industry really stepping up to incentivise and encourage this; many buyers will have hurried to place orders before planned manufacturer price rises in April.”
The UK’s best-selling model last month was the Ford Fiesta, followed by the Vauxhall Corsa and Volkswagen Golf in the second and third slots.
Sean Kemple, director of sales at Close Brothers Motor Finance, said: “This fall in car sales will come as something of a surprise to the sector, which was expecting a slight increase on last year’s low figures.
“Registrations continue to slump, remaining far lower than those of two years ago when we saw a spike as the VED road tax changes took effect. Consumer confidence in the face of Brexit uncertainty is certainly not what it was a few years ago, and we still have some road ahead before we reach those levels again.”
He added: “There is cause for optimism though. For the past two months, we’ve seen gradual improvements in demand for alternatively fuelled vehicles.
“Appetite is clearly there, and the wheels are still turning. The consumer is becoming more aware of the benefits of AFVs or an electric vehicle, and manufacturers are responding to this demand.”