BMW has said it will be forced to close its production sites in the UK, putting 8,000 jobs at risk, if components for Mini and Rolls-Royce cars are caught up in customs delays after Brexit.

In its starkest warning over Brexit yet, the customs manager of the German carmaker’s UK operations said its manufacturing set-up would not be able to cope with obstructions to its supply chain.

“We always said we can do our best and prepare everything, but if, at the end of the day the supply chain will have a stop at the border, then we cannot produce our products in the UK,” Stephan Freismuth told the Financial Times.

BMW employs 8,000 people in the UK, including 4,500 at its flagship plant in Cowley, Oxford, where it produces the Mini.

The BMW warning comes ahead of of a key motor manufacturing industry conference on Tuesday where a series of automotive executives from companies with major UK manufacturing operations are expected to express serious concerns about the future of their businesses.

The industry hopes a series of warnings from companies including Honda, Volvo and Ford will act as a wake-up call to Theresa May who made exiting the customs union and the single market one of her early red lines.

Freismuth said: “We don’t want to give up our UK plants. We do our best to maintain business continuity.” He added: “If you have a stop for one day, it costs a lot of money, but at the end if there are more stops our management has to decide how this can be sorted.”

BMW has four plants in the UK, including a Rolls-Royce assembly unit in Goodwood in Sussex and an engine plant at Hams Hall in Birmingham. It also has a metal-pressing facility in Swindon.

On Saturday thousands of workers enjoyed a summer family fair at the flagship Mini plant in Oxford where food, a ferris wheel and music were laid on by the company. A full or part closure would have a devastating impact for the surrounding area, the poorest part of Oxford, which relies heavily on BMW for employment.

The car industry employs about 860,000 people in the UK with virtually all production relying on just-in-time processes, the term used to describe components arriving seamlessly from multiple domestic and international destinations in order to avoid costly stockpiling of parts.

The port of Dover and Getlink, which runs Eurotunnel, have said even a two-minute delay at the ports could mean queues up to 17-miles long, with severe consequences for all just-in-time production and the supply of fresh produce.

BMW’s warning came just days after Airbus, an important employer in Wales and the Bristol area, said it would be forced to leave the UK if Brexit leads to its operations becoming uncompetitive. The Airbus intervention on Friday was initially greeted with dismay by the government, with the health secretary, Jeremy Hunt, castigating the Franco-German maker of the A380 aircraft for making “inappropriate” remarks.

The foreign secretary, Boris Johnson, was also reported to have reacted privately by saying, “Fuck business.”

Last week the port of Dover warned there could be emergency traffic congestion management, including turning parts of the M20 into a lorry park, if there were any delays at the port.

On Tuesday morning the chief executive of the society of Motor Manufacturers and Trade is expected to open the trade body’s automotive summit with a strong message to the government.

The Japanese ambassador to Britain is also scheduled to speak and is expected to voice concern about the future of Nissan’s Sunderland factory, Toyota’s Derby operations, and Honda’s Swindon site post-Brexit.

BMW’s warning came hours after business leaders from the US, Canada, Japan and India told the British government to solve the Brexit issue urgently or put more than £100bn worth of trade at risk.