A formal battle for the UK Labour Party leadership edged closer after both main contenders to unseat prime minister Keir Starmer made big moves on Thursday.

Wes Streeting resigned from his role as health secretary, saying he had “lost confidence” in Starmer’s leadership and could no longer serve in his cabinet. Streeting did not declare that he would formally challenge the UK prime minister, but his allies were openly drumming up support among Labour MPs in Westminster.

In his resignation letter, Streeting also said “the debate that comes next … needs the best possible field of candidates”. This appeared to be a coded way of saying any future leadership contest should include other contenders such as Greater Manchester mayor Andy Burnham, who is currently blocked from running as he is not an MP.

Meanwhile, Burnham unveiled his strategy to solve that very issue by announcing his intention to seek permission from the Labour Party’s ruling national executive committee (NEC) to run in a byelection in Makerfield near Wigan, 30km from Manchester.

Burnham had been seeking a Labour MP to stand aside to let him run ever since the party’s NEC, stacked with Starmer’s allies, blocked his last byelection bid in Gorton & Denton.

Labour lost the subsequent battle for that seat to the Greens, as the party was beaten into third place by Nigel Farage’s Reform UK.

Win or bust: Andy Burnham’s risky return bid could decide Labour’s futureOpens in new window ]

Westminster had been consumed in recent days with speculation about which constituency in the vicinity of Burnham’s Manchester patch he might secure for a byelection bid, which could unlock his route back to parliament to challenge Starmer.

A succession of MPs in the wider region, such as Charlotte Nichols in Warrington North and Afzal Khan in Manchester Rusholme, denied they would give up their seats to allow Burnham a shot back at parliament.

Allies of Starmer, who has vowed to fight any attempt to unseat him, began briefing that Burnham did not, in fact, have any route back to Westminster and argued he would not figure in any leadership battle.

However, shortly after 5pm, Josh Simons, MP for Makerfield, said he would make way for Burnham and backed the Greater Manchester mayor to “drive the change [Britain] is crying out for”.

Minutes later, Burnham confirmed he would ask Labour’s NEC for permission to run in the byelection, where he would face a strong challenge from Reform UK.

Burnham said he planned to deliver political change at “a national level”, all but confirming he wanted to be prime minister. The NEC, which also controls the timetable for any leadership election, is due to meet on Tuesday.

Earlier on Thursday, former deputy prime minister Angela Rayner in effect announced her return to frontline politics after she resigned last September for underpaying tax on a flat.

She said she has been cleared of deliberate wrongdoing by tax authorities this week, has paid any tax owed, and is ready to return to the fray.

She also said Labour’s NEC should allow Burnham to run in any upcoming byelection. He was recently photographed exiting her flat, where the two were assumed to have held discussions about the future of the Labour Party and its leadership.