Rebecca Long-Bailey is expected to win the backing of Momentum as a poll placed her ahead of closest rival for the Labour leadership, Keir Starmer.

The shadow business secretary, who has been criticised for the slow start to her campaign, came out ahead of the shadow Brexit secretary based on first preferences, with 42% of the votes compared to his 37% in the poll, conducted by Survation of more than 3,800 LabourList readers .

Although Starmer receives the majority of second preferences from all candidates in the race, they are not enough to eliminate Long-Bailey’s first round lead, with the overall result at 51 % to 49 % after second preferences are taken into account.

The poll will be viewed as a boost for Long-Bailey, who was well behind in a previous poll by YouGov for the Party Members Project that had her losing to Starmer by 61% to 39% in the last round.

The new poll was weighted to reflect the party as a whole by age, sex, and UK region, and took place between 8 and 13 January. LabourList readers are likely to be more engaged in the race than the membership as a whole at this stage.

The polling comes ahead of Long-Bailey’s official launch to be leader later this week, and the expectation that Momentum members will endorse her as their preferred candidate. The group asked members if they agree with senior officials who chose to back the shadow business secretary as his replacement.

A senior Momentum source said the decision made by the group’s National Coordinating Group to endorse the Salford and Eccles MP for leader was unanimous. She is considered to be the most leftwing of the five contenders, and a Corbynite successor. Winning the backing of up to 40,000 Momentum activists would be considered a significant boost for her campaign.

However, the formulation of the question posed to members, a simple yes or no to Long-Bailey, sparked anger among members, who think it should have been an open ballot and active for longer than 48 hours.

The senior source said they accepted that people were unhappy with the process but that there was no disagreement on who best represented the organisation’s leftwing values after Clive Lewis dropped out of the race.

“There’s people who don’t agree with the way it’s been done, but they do think the candidate should be Rebecca Long-Bailey,” the source said.

Part of the unease among members is the significant influence of chair of the organisation, Jon Lansman, who is also working on Long-Bailey’s leadership campaign.

One disgruntled member, who has campaigned extensively for Corbyn, told the Guardian: “She is the most leftwing candidate, so I would imagine that she would get an easy pass through the ballot.

“But how little do you trust in the membership that you won’t make it an open process? Given the movement is about democratising the Labour party as well. People are really cross among the membership about this.”

Momentum activist Michael Chessum wrote on Twitter: “Momentum is balloting its members on the Labour leadership and deputy leadership election. Ludicrously, we only have one option for each position. This is a joke, and you should vote no on principle (even if, like me, you might end up voting for one of the chosen candidates).”

Concern has also been raised among some Momentum members about Long-Bailey’s decision to unequivocally back the Board of Deputies of British Jews’ 10 pledges for Labour leadership and deputy leadership candidates. They fear the 10 commitments could potentially close down the debate on Palestinian rights.

Towards the end of the week, Momentum is expected to launch a full-scale campaign to support Long-Bailey if she gets the members’ endorsement, deploying its social media team, film-makers and organisers to push her campaign against Starmer, who is the favourite according to most polls.

The survey of Labour party members commissioned from YouGov by the Party Members Project run out of Queen Mary University of London and Sussex University, has Long-Bailey as the frontrunner among Momentum members specifically at 26.6%.