Japanese carmaker Honda said any delay to Brexit must be long enough to give businesses stability.
The UK's car sector, which employs more than 850,000 people, has quickly gone from a manufacturing success story to posting drops in investment, sales and output.
Honda, which builds just over 10% of Britain's 1.5 million cars, announced earlier this year that it would close its factory in Sunderland.
This was the biggest blow to the sector in many years, but Honda said the decision was not due to Brexit.
Adding to uncertainty for companies, British politicians voted overwhelmingly last night to seek a delay to Brexit, which had been due on March 29.
"We are now looking to the government to deliver a clear, legally certain, path forward to avoid no deal," a Honda spokesman said.
"Any extension must be purposeful and long enough to give business stability," he added.
Since Britain voted in June 2016 to leave the European Union, companies have been triggering a series of contingency plans to help prepare for any loss of free and unfettered trade with the car industry's biggest export market.
Honda, BMW's Mini and Rolls-Royce brands and Jaguar Land Rover – together accounting for around 55% of UK car output – all plan to shut their factories in April from between a week to up to a month in case of any disruption from a no-deal Brexit.
A delay would ruin such plans as shutdowns are generally organised months in advance so employee holidays can be scheduled and suppliers can adjust volumes.