Michael Gove, the former justice secretary and prominent leave campaigner, has held a personal meeting with Donald Trump, and written about it for the Times.

Gove, who has a regular column with the newspaper he worked for before being elected as MP for Surrey Heath, was co-chair of campaign group Vote Leave, and his decision to stand for the Conservative leadership scuppered the hopes of Boris Johnson.

News that Gove and the US president-elect have met for an interview that will appear in the Times on Monday is likely to irritate No 10, which has carefully been laying the groundwork for the prime minister to travel to Washington DC to visit Trump, perhaps as soon as next month.

President-elect @realDonaldTrump gives his first UK interview to @michaelgove, available from 10pm on https://t.co/GiHiNxrYJ5 pic.twitter.com/NYakH7NcT7 — The Times of London (@thetimes) January 15, 2017

The interview was conducted along with a journalist from German newspaper Bild. Trailing the contents before its 10pm online publication, the newspaper’s publisher, Kai Diekmann, suggested that BMW formed at least one part of the discussion.

May sacked Gove, along with longtime allies including George Osborne, in the reshuffle she carried out when she became prime minister last July.

Britain’s relationship with the US is likely to be crucial as May’s government prepares for life outside the EU. Trump has suggested he would be keen to strike a trade deal with the UK, in striking contrast to Barack Obama, who said during the referendum campaign that Britain would be at “the back of the queue” for trade talks if it voted for Brexit.

Boris Johnson, the foreign secretary, has held meetings with key members of Trump’s transition team in Washington, and May’s two closest advisers, Fiona Hill and Nick Timothy, have also visited. The publication of Gove’s interview with Trump comes as the prime minister prepares to set out her aims in Brexit negotiations in a major speech on Tuesday.

Gove is known to be close to Rupert Murdoch and news that he has secured an interview will prompt speculation that it was brokered by the media magnate, whose Fox News network gave favourable coverage to Trump’s campaign.

Asked about the interview, a No 10 insider said it “sounds like a good read”.