Britain’s new government found itself on a collision course with former President Donald J. Trump on Wednesday after his campaign filed a complaint that accused the governing Labour Party of interfering in the American presidential election by recruiting volunteers to canvass for Vice President Kamala Harris in battleground states.

In a letter to the Federal Election Commission dated Monday, a lawyer for the Trump campaign said that Labour’s recruitment of volunteers, as well as recent meetings in which Labour officials offered advice to the Harris campaign, constituted “blatant foreign interference” in the election.

Prime Minister Keir Starmer brushed off the accusations, saying that Labour activists had worked on an unpaid basis in multiple American elections. Mr. Starmer, who had dinner with Mr. Trump during a recent visit to New York, said the issue would not poison their relations if Mr. Trump were elected.

“As prime minister of the United Kingdom, I will work with whoever the American people return as their president in their elections, which are very close now,” Mr. Starmer told reporters on his way to a diplomatic gathering in Samoa.