He said the publication of his memos regarding the Trump administration had made it "impossible" for him to carry on.
The Tory leadership contenders had differing views regarding Sir Kim Darroch's future as British ambassador to Washington.
Sir Christopher Meyer said the source of a leak of private government emails should "think carefully" before divulging anything else.
The PM has insisted the British ambassador to the US has her full support, despite Donald Trump saying he would no longer work with him.
The Tory MP said the leak of private messages from Sir Kim Darroch to the UK government was a "betrayal" of the country.
The US president has hit out at the UK's ambassador to Washington, who said in leaked emails that the Trump administration was "inept".
Paul Golding said the interest in the group had risen as a row between Theresa May and the US president increases