U.S. President Donald Trump said a free trade deal with Britain might be impossible if London went ahead with Prime Minister Theresa May's proposals for post-Brexit ties with the European Union, in damaging remarks that could widen domestic criticism of her plans.

In an interview with Britain's Sun newspaper published late on Thursday, Trump said May's plans for a business-friendly Brexit would leave it too close to the EU to allow a new trans-Atlantic trade deal to be struck.

Just hours earlier at a lavish dinner to mark Trump's first visit to Britain as president, May made a direct pitch for a deal with Washington. She praised the friendship between the two allies, glossing over Trump's previous remarks that Britain was a "hot spot" in turmoil over Brexit.