Auto manufacturers produced 440,426 cars in the January to March period, down 6.3 percent from a year earlier.
In March alone, the year-on-year pace of decline accelerated to 13.3 percent as bad weather disrupted supply chains.
"A double-digit decline in car manufacturing ... is of considerable concern," Mike Hawes, chief executive of the Society of Motor Manufacturers and Traders, said on Thursday.
Four out of five cars built in Britain are exported. But the quarter's decline was led by a fall in production for the domestic market - which dropped by 14.1 percent - versus a smaller reduction of 4 percent in vehicles made for export.
British consumers' disposable income has been squeezed by a year of high inflation, triggered by the pound's fall after the Brexit vote in June 2016, and some have held off buying diesel cars due to concern about environmental damage and green taxes.
"Following recent announcements on jobs cutbacks in the sector, it's vitally important that the industry and consumers receive greater certainty, both about future policies towards diesel and other low emission technologies, and our post-Brexit trading relationships," Hawes said.
Nissan and Jaguar Land Rover are both cutting jobs, according to industry sources who blamed a lack of domestic demand for diesel cars in particular.
Thursday's figures add to signs that British economic growth is likely to show a slowdown when preliminary first-quarter gross domestic product figures are released on Friday.
A particularly sharp slowdown could further weaken the chances that the Bank of England will go ahead with a once widely expected interest rate rise next month, only the second since the 2008 financial crisis.
However, many economists think that the BoE will wait to see if there is a pick-up in April business surveys before reaching a final decision.
Last month, Prime Minister Theresa May reached an outline agreement with the European Union to preserve existing trade relationships until the end of 2020. But she has said that in the longer term she does not want a customs union with the EU, which car makers fear will disrupt their supply chains.
(Reporting by David Milliken; Editing by Alison Williams)