LONDON — British Prime Minister Andy Burnham insisted on Tuesday he handled a message back-and-forth with someone impersonating Donald Trump’s chief of staff in the “right way.”

He told broadcasters he is not embarrassed by the incident, reiterating that “nothing of consequence” was discussed.

POLITICO first reported Monday that the U.K. prime minister had engaged with messages from somebody pretending to be Susie Wiles, a top adviser to the U.S. president. The key aide has previously been the victim of a phone hack, although the White House said the two incidents were not connected.