Theresa May has bowed to intense pressure from her own party and named 7 June as the day she will step aside as Conservative leader, drawing her turbulent three-year premiership to a close.

Speaking in Downing Street, May said it had been “the honour of my life” to serve as Britain’s second female prime minister. Her voice breaking, she said she would leave “with no ill will, but with enormous and enduring gratitude to have had the opportunity to serve the country I love”.

The prime minister listed a series of what she said were her government’s achievements, including tackling the deficit, reducing unemployment and boosting funding for mental health.

But she admitted: “It is and will always remain a matter of deep regret to me that I have not been able to deliver Brexit.”

May’s announcement came after a meeting with Graham Brady, the chair of the backbench Tory 1922 Committee, which was prepared to trigger a second vote of no confidence in her leadership if she refused to resign.

Her fate was sealed after a 10-point “new Brexit deal”, announced in a speech on Tuesday, infuriated Tory backbenchers and many of her own cabinet – while falling flat with the Labour MPs it was meant to persuade.

The leader of the House of Commons, Andrea Leadsom, resigned on Wednesday, rather than present the Brexit bill to parliament.

A string of other cabinet ministers had also expressed concerns, including Sajid Javid, Jeremy Hunt, Chris Grayling and David Mundell.

In particular, they rejected May’s promise to give MPs a vote on a second referendum as the Brexit bill passed through parliament, and implement the result – which they felt came too close to endorsing the idea.

The former foreign secretary Boris Johnson is the frontrunner to be Britain’s next prime minister, but more than a dozen senior Tory figures are considering throwing their hats into the ring.

In the cabinet, Rory Stewart has already said he will stand, while Jeremy Hunt, Michael Gove, Penny Mordaunt and Sajid Javid are all likely contenders.

May’s departure came after three years of wrangling with Brexiters on her own backbenches about what future relationship with the European Union they would be prepared to accept.

That became considerably more difficult when she lost her majority at the 2017 general election, after spearheading what was widely regarded as a disastrous campaign, promising “strong and stable leadership in the national interest”.

Brexit is likely to dominate the race to succeed May, with time increasingly tight for a new team to set out any new direction before the deadline of 31 October for Britain’s departure from the EU.

May’s longtime friend Damian Green, the former first secretary of state, defended her record on Friday.

He said: “All prime ministers, in the end, take responsibility for what happens on their watch, but I think that it’s undeniable that suddenly and unexpectedly becoming prime minister after the seismic shock of the Brexit referendum meant that she was dealt an extremely difficult hand to play. And the truth is that having an election a year later, which cut the Conservative party’s majority, then [made it] impossible.”

Green told BBC Radio 4’s Today programme: “The fact that parliament has not been able to get a Brexit deal through has led to the impatience, bordering into contempt, for the political class and the amount of hostility and borderline violence is something we have not known for a very very long time.”