Andy Burnham would have won the Gorton and Denton byelection, Labour’s deputy leader said as she called for the party to make more use of the Greater Manchester mayor.

Overturning a 13,000 Labour majority from the general election, Hannah Spencer, a local plumber and Green councillor, became the party’s fifth MP on Friday in an area that had returned Labour MPs for nearly a century.

Reform UK’s Matt Goodwin was second, just ahead of the Labour candidate, Angeliki Stogia.

The result has prompted renewed questioning of the party’s decision to block Burnham from contesting the seat last month.

Speaking to the BBC’s Newscast podcast, Labour’s deputy leader, Lucy Powell, said Burnham “probably would have” held the seat.

She said: “I think certainly the Greens wouldn’t have gone after the seat in the same way that they did.”

Powell was the only member of Labour’s ruling national executive committee to vote in favour of allowing Burnham to stand in Gorton and Denton, with eight others including Keir Starmer voting against.

But she told the BBC she accepted “collective responsibility” for the decision, citing concern about a mayoral byelection in Greater Manchester.

Powell also said her party needed to draw inspiration from the reasons for Burnham’s popularity in Greater Manchester, saying people “see in him someone who is on their side, someone who is delivering those Labour values and those Labour policies”.

She added: “We have to draw on that, make use of Andy Burnham, but also draw on that and reflect on how we could do that better nationally and better as a Government.

“And I know from talking to Keir many, many times over recent weeks, before this byelection and since, that that is something he is very focused on doing.”

Burnham is understood not to have ruled out having another go at returning to parliament. “With all the chaos and turmoil, who knows what might happen. It would be foolish to say he would never,” one ally said.

Burnham himself is yet to comment on the result in Gorton and Denton, while Starmer has vowed to fight on despite the “disappointing” outcome of the poll.

Angela Rayner, the former deputy prime minister and a key figure on Labour’s left, called the byelection result “a wake-up call”.

Meanwhile, the home secretary, Shabana Mahmood, is expected to warn against moving to the left in response to the byelection as she introduces legislation for tougher immigration measures next week.

A source close to the home secretary told the Times: “The Labour government should not learn the wrong lessons from its recent byelection loss.

“The idea that we are losing Muslim voters over immigration is just plain wrong.”