Controversial plans that would make it easier for Labour members to deselect sitting MPs are likely to be passed at the party conference next week with the backing of Unite and other unions, a key ally of Jeremy Corbyn has predicted.

The claim, which will alarm MPs already worried about being purged, was made by the Corbynite MP Chris Williamson at a party meeting last month, a recording of which has been passed to the Observer.

The issue of whether conference will back what is called “mandatory reselection” – under which MPs wanting to stand at another election would have to face full selection contests that would be open to other candidates – is one of the most contentious facing delegates in Liverpool.

Critics of the plan say it would leave MPs too vulnerable to purges, while supporters insist it would ensure the views of local members and MPs are aligned, and be a big step towards a truly democratic, member-led party.

At present, Labour MPs only face an open selection process if a majority of local ward and union branches affiliated to their local party fail to support them in “trigger ballots”, which happen in advance of elections. Sitting MPs rarely fail to win these, because to rally so many branches involves a big negative campaign across a constituency. John McDonnell, the shadow chancellor, has said repeatedly that he is happy with trigger ballots and does not support a change.

But many MPs believe there is support for open selections from many Corbyn backers and within Unite. So sensitive is the issue that both Corbyn’s office and Unite, which wields a large section of the vote at conference, have yet to decide whether they will support the idea at next week’s gathering in Liverpool.

But during a “democracy roadshow” round the country promoting reform, Williamson, who is seen as a Corbyn outrider, told a meeting in Barnsley on 22 August that he believed the plans would be voted through with the help of Unite.

Play Video Labour's Chris Williamson on mandatory reselection - audio

Williamson told the meeting he was a strong supporter of mandatory reselection, which, he argued, would be “uplifting” for MPs, who would benefit from receiving endorsements from ballots of members. “I think that Unite are likely to support it and some of the smaller unions will definitely support it. The FBU [Fire Brigades Union], Aslef [the train drivers’ union] and the CWU [Communication Workers Union],” he said.

“So I think we will get this through and I think that it will have a hugely democratising effect on our party.”

Labour MP Angela Smith, in whose constituency the meeting was held, said the way Williamson was encouraging members to vote for the change, and his claim to know how Unite would vote, showed how real the threat was to sitting MPs.

Smith, who is a member of the committee of Labour MPs that relays their views to the leader’s office, said: “Chris Williamson’s assertions, combined with Jeremy Corbyn’s refusal to tell me what his own view is of mandatory selection, lead me to believe that the future of the Labour party is now seriously under threat.

“There is still time for Corbyn to distance himself from Williamson’s aggressive campaign. A message from him to the national executive committee this week, to the effect that he will not support this undermining of his parliamentary Labour party colleagues, would go a long way towards rebuilding party unity.’’

A Unite source said that while the union had supported mandatory reselection two years ago, its delegates would have to decide how to vote after seeing the precise wording of any motion. Labour sources say the leadership “has no position for or against mandatory reselection” and that it will be left up to the conference to decide. The matter is, however, expected to be discussed at a meeting of the national executive committee this week.

The pro-Corbyn grassroots group Momentum said a petition in support of “open selections” had passed 10,000 signatures.

The campaign follows Momentum’s recent support for an “open, inclusive selection process which would open the door to a new generation of MPs”.

Momentum argues that an “outdated rulebook” is holding back new members, and that Labour’s selection procedure should be “democratic, give a fair chance to all candidates and encourage positive campaigning”.

Laura Parker, Momentum’s national co-ordinator, said: “Nearly 10,000 signatures in less than four days shows the desire Labour members have for overhauling our outdated rulebook and opening up the process of how we choose our MPs to give a fair chance to all candidates.

“We must open the door to a new generation of MPs, end the jobs-for-life culture and allow those who have been organising in their communities for years the chance to also represent them in Westminster.

“We should also remember the collective knowledge and campaigning power of Labour’s membership is our greatest asset, and it would be a great betrayal of the members if open selections weren’t properly debated at party conference.”

Contacted on Saturday by the Observer, Williamson said there was now overwhelming support within the party for the change.