Wes Streeting has said he would be prepared to challenge Keir Starmer and spark a Labour leadership contest as early as next week.

The former health secretary, who quit the cabinet last month, said “uncertainty and paralysis” would have to be ended and that he would give the prime minister at least the weekend to think about it.

The intervention by Streeting came as voters in Makerfield prepare to go to the polls in a byelection on Thursday that Andy Burnham, the mayor of Greater Manchester, hopes to use as a springboard back into parliament ahead of a leadership tilt. Polls show he is leading Reform UK in the Greater Manchester constituency.

While it is Burnham’s intention to seek to replace Starmer as prime minister as early as possible, his supporters are sceptical of Streeting’s bullishness about a contest and have cast doubt on whether he has the support of the 81 Labour MPs need to trigger a leadership contest.

Nevertheless, when asked on BBC Two’s Newsnight on Wednesday night if he would trigger a contest if Burnham wins, Streeting said: “I think the prime minister should be given some space and time to reflect over the weekend and I think we should see where we are then.

“I would prefer the prime minister to take a decision on his own terms rather than leave it for me or Andy or anyone else to trigger a contest. If not, we can’t carry on with this uncertainty and paralysis and there will need to be a contest and I would be prepared to do that.”

Streeting had held back on issuing the warning that he would trigger a contest when he gave a speech earlier on Tuesday in London where he argued for a “progressive capitalist” approach.

He insisted he did have the support of 81 Labour MPs and warned those who would stand against him that Labour members would be able to “smell inauthenticity” where “people are trying to tack left, adopt one position one day and another position another day”.

Starmer, who is currently in France at the G7, would automatically be a candidate in any Labour leadership contest.

The Cabinet Office minister, Nick Thomas-Symonds, would not be drawn on whether a Labour leadership challenge would begin next week.

Asked whether he expected Streeting to launch a challenge next week, he told Sky News: “I’m not Nostradamus.”

He added: “All I would say is, if you look at this week, on Monday the government announced a social media ban for under-16s. At the G7, the prime minister has just secured £1.3bn of investment into the UK, creating over 1,400 jobs.”