Toyota Motor Corp. and Nissan Motor Co. say they'll keep making cars in the U.K. despite Prime Minister Theresa May's plan to leave the European Union's single market, which could make exporting from British factories less lucrative.

May's Brexit plan, outlined Tuesday, won't derail Nissan's commitment to build new versions of its Qashqai and X-Trail sport utility vehicles at its factory in Sunderland, England, Chairman Carlos Ghosn said Wednesday. Toyota plans to keep its car- and engine-building plants in the U.K. and may take steps to increase their competitiveness if leaving the European Union raises costs, Chairman Takeshi Uchiyamada said.

"We can survive this," Uchiyamada said in an interview at the World Economic Forum in Davos, Switzerland. "In every country in the world, we don't tend to close or move factories when things like this happen and it will be the same in the U.K."