WASHINGTON — Just before his state visit to Britain was to begin, President Trump subverted diplomatic norms by rattling an already precarious political situation there: He suggested that the next prime minister of Britain “walk away” from trying to reach a deal to withdraw from the European Union and that the far-right populist Nigel Farage be sent in to negotiate.

In an interview with The Sunday Times, of London, Mr. Trump also said he had told the current prime minister, Theresa May, who announced last month that she would step down after repeatedly failing to get her Brexit plan through Parliament, to sue the bloc for greater leverage in talks. Mrs. May left her government in a weaker position, he said, for not threatening to walk away “in the form of litigation or in the form of a request.”

The president and Melania Trump, the first lady, are set to arrive in London on Monday for a full state visit, which Mrs. May had been trying to arrange for years. Coincidentally, it will be her last week as the leader of the Conservative Party. With the government five months away from an exit deadline, uncertainly looms over her potential successor. The British economy has also taken several hits, which businesses have blamed on Brexit.

Across the Atlantic, Mr. Trump’s comments only reinforced the degree of instability.

In the interview, the president posed the idea that Mr. Farage, the leader of the newly founded Brexit Party who has been a battering ram to traditional conservative politics in Britain and a rival and irritant to Mrs. May, should take over the negotiations.