The first-ever woman to become deputy leader of the Labour party has said “nobody in their right mind would want” the position, which she described as “a terrible job, really ghastly”.

Dame Margaret Beckett held the role from 1992 to 1994, but told the BBC she “certainly didn’t want” the job and was “pushed” into running to be the-then leader John Smith’s deputy.

Speaking after the resignation of Angela Rayner, the former Derby South MP said: “It’s a lot of time, it’s a lot of work, it’s a lot of responsibility, and it’s thankless.”

Candidates are now emerging in the race to replace Rayner, who also stepped down from her government jobs as deputy prime minister and housing secretary.

Speaking to the BBC on Wednesday, Dame Margaret said Smith, who died in 1994, “threw” work he did not consider a priority for the leader in her direction.

“I had seen at quite close quarters what it meant for [her predecessor, former deputy leader] Roy Hattersley,” she added.

“You were always on the graveyard slot when there were ghastly by-elections.”

Despite the challenges of the role, Dame Margaret stressed the importance of the deputy leader working alongside the leader rather than being critical.

“What you’ve got to do is to make a constructive leadership team that can help and support getting the party in the right place, so that the government can be in the right place, so that the country can be in the right place,” she said.

“That’s what’s important, not childish games.”

Asked whether Rayner, who resigned after admitting she failed to pay enough tax when buying a £800,000 flat in Hove, had done a good job, Dame Margaret said: “Angela had, I think, some problems with it, but that’s partly because of some of the people around her who tried to make her somebody who was kind of an alternative, or critical of [Keir Starmer].

“That’s not good. That’s not what the job’s about, and it shouldn’t be.”

Candidates to replace Rayner have until Thursday evening to win the backing of at least 80 Labour MPs, and will then need support from either 5% of local parties or three Labour-affiliated groups, including two unions.

The winner will then be decided in a vote of party members, with an announcement due on 25 October.

David Lammy will remain deputy prime minister, regardless of who wins.

Education secretary and MP for Houghton and Sunderland South Bridget Phillipson and South London MP Bell Ribeiro-Addy are among the candidates.

Manchester Central MP Lucy Powell and former shadow foreign secretary Dame Emily Thornberry are also in the running along with Housing Minister Alison McGovern and Liverpool Wavertree MP Paula Barker.

Dame Margaret, who rose to be foreign secretary under Sir Tony Blair, would not be drawn on which of the current deputy leadership candidates she supported.

“I shall wait and see what the full slate is,” she said.

She added her advice for the winner would be to “take it seriously” and “don’t demonstrate your importance by being rude to everybody”.

Additional reporting by Dan Martin