Catherine West, the Labour MP who announced a challenge to Keir Starmer’s leadership, has changed course to say she instead wants the prime minister to set a timetable of September for his departure.

West, the MP for Hornsey and Friern Barnet and a former Foreign Office minister, announced on Saturday that she would seek to gather the 81 Labour MPs’ names needed to formally challenge Starmer, saying this was just a device to tempt others to stand and that she did not wish to take over.

In a statement released after Starmer’s speech on Monday morning in which he said he would fight on despite terrible results for Labour in elections last week, West called for an orderly process for Starmer to depart. She said: “I have listened to the prime minister’s speech this morning. I welcome the renewed energy and ideas. However, I have reluctantly concluded that this morning’s speech was too little, too late.

“The results last Thursday show that the prime minister has failed to inspire hope. What is best for the party and country now is for an orderly transition. I am hereby giving notice to No 10 that I am collecting names of Labour MPs to call on the prime minister to set a timetable for the election of a new leader in September.”

Under Labour rules, at least 81 MPs, or 20% of the total parliamentary party, need to back a challenge for one to happen. This means West’s plan to simply gather names calling for a future contest would have no force under the rules, but would instead act as a de facto no-confidence vote.

West’s change of plan potentially takes some of the urgency out of the situation, amid speculation that expected rivals such as Wes Streeting, the health secretary, and Angela Rayner, Starmer’s former deputy, would launch imminent bids.

The prospect of a longer timetable would allow time for Andy Burnham, the mayor of Greater Manchester, to potentially return to parliament and join the contest although after his speech, Starmer said whether he would be allowed to do this was still a matter for Labour’s national executive committee (NEC), which blocked him in January.

Speaking to a conference of the Communication Workers Union in Bournemouth on Monday, Rayner said Burnham should not have been stopped from contesting the Gorton and Denton byelection, which Labour then lost. “It was a mistake that the leadership of our party should put right,” Rayner said. She said Labour should put “the common interests ahead of factionalism”.

In what was widely billed as a make-or-break speech in London on Monday morning, Starmer said he would fight any leadership challenge and would not walk away from his responsibilities as prime minister.

He promised he would seek a new deal with the EU including a sweeping youth mobility scheme, as well as nationalising British steel and promising a beefed-up youth guarantee of jobs and apprenticeships.

But he warned his critics in the party they risked opening the door to Nigel Farage’s Reform UK party and said it was time to take a more robust approach to the right. “We are not just facing dangerous times, but dangerous opponents, very dangerous opponents,” he said, saying Labour was the last defence against the country heading down a “very dark path”.