May faces a split in her Conservative Party, with some influential figures preferring a more complete break with the EU than she is advocating. Roughly 50 hard-liners met Tuesday night to discuss her possible ouster.
In the interview, May said the leadership talk can be distracting. "I get a little bit irritated, but this debate is not about my future. This debate is about the future of the people of the U.K. and the future of the United Kingdom," she said. "That's what I'm focused on, and that's what we should all be focused on."
The opposition Labour Party is also increasingly divided over the Brexit issue. London Mayor Sadiq Khan broke ranks on Sunday with party leader Jeremy Corbyn to publicly back a second referendum of whether Britain should go forward with plans to leave the EU.
Writing in The Observer, Khan said Britain faces either a bad deal or no deal at all — options he said are "incredibly risky." He said the public deserves a right to choose between any deal reached by the government or staying in the EU. He said that if no deal is reach, the public should be able to choose between the "no deal" scenario or remaining in the bloc.
The mayor's stance is expected to put more pressure on Corbyn at the Labour Party conference later this month. In her interview, May criticized former Foreign Secretary Boris Johnson, who resigned in July to protest her plan to keep some close ties to the EU after Brexit.
Johnson, who is seen by many analysts as positioning himself as a possible successor to the embattled prime minister, recently caused a furor by comparing May's Brexit strategy to a "suicide vest." "I have to say that that choice of language is completely inappropriate," May said.