Emily Thornberry and Paula Barker have both withdrawn from the Labour deputy leadership contest, leaving three candidates left in the race to replace Angela Rayner.

In order to progress to the next stage in the contest, MPs need to get the backing of 80 MPs by Thursday afternoon – a bar Thornberry and Barker looked unlikely to clear.

It is also doubtful that backbench MP Bell Riberio-Addy will garner enough support before the 5pm deadline.

Education Secretary Bridget Phillipson and former minister Lucy Powell are the two candidates expected to make it to the next stage.

Announcing her decision to step down on social media, Thornberry said she was “deeply grateful” to Labour members for their support and added that it had been “a privilege to take part in this race with such brilliant women”.

Barker said the next deputy leader should listen to members and must “not be afraid to bring those challenges to the government”.

“Being a good team doesn’t mean we can’t be honest – criticism of government, when it’s constructive, makes us stronger,” she added.

Barker is now throwing her supporter behind Lucy Powell, who she said could be “a constructive friend to the government”.

Housing Minister Alison McGovern withdrew from the race on Wednesday and backed Phillipson after failing to pick up enough support.

In order to make it to the final ballot, deputy hopefuls will have to win the backing of 5% of local parties or three Labour affiliated groups, such as a trade union.

Voting opens on 8 October and closes on 23 October, with the winner being announced two days later.

Candidates will have the chance to make their pitch to Labour members at hustings during the party’s conference, which takes place at the end of September.

The contest is an unwelcome distraction for Prime Minister Sir Keir Starmer, as it has the potential to become a vehicle for unhappy MPs and party members to express their discontent with the leadership.

Phillipson’s position as the only cabinet member in the race has helped her secure nominations from those MPs who are loyal to the government.

However, it could harm her in the eyes of party members, who may prefer a candidate who can be independent of the leadership.

Both Riberio-Addy and Barker have been critical of the government, with both criticising its position on the war in Gaza.

Riberio-Addy has acknowledged she is unlikely to win the contest but wanted to encourage a debate among Labour member about “what’s gone wrong” in the party’s first year in power.

Many senior Labour figures have said the next leader should be a woman and from outside London to counter what they see as the London-centric and male-dominated party leadership.

Whatever the result, the deputy leader will not become deputy prime minister, as Sir Keir has already appointed David Lammy to the role.

Both positions became vacant after Angela Rayner resigned having admitted that she did not pay enough tax on her £800,000 flat in Hove.

Sir Laurie Magnus, the PM’s ethics adviser, found she did get legal advice when buying the property, but failed to seek further expert tax advice as recommended.

Rayner said she took “full responsibility for this error”, adding: “It was never my intention to do anything other than pay the right amount.”