The Labour leadership contender Rebecca Long-Bailey has written to leading figures in Momentum, urging the leftwing campaign group to throw its weight behind Angela Rayner as the party’s deputy leader.

Momentum’s coordinating committee is expected to meet on Saturday to decide which candidates it will support for the leadership and deputy leadership.

Long-Bailey is highly likely to be their choice for leader, not least because the group’s founder Jon Lansman is advising her – but it is unclear which candidate the powerful group will back for deputy.

In a letter seen by the Guardian, Long-Bailey calls for Momentum to throw its formidable campaigning machinery behind Rayner – instead of supporting Corbynite favourite Richard Burgon.

Burgon, secretary of the Campaign Group of socialist MPs, is backed by Long-Bailey’s longtime mentor, John McDonnell, as well as staunch Corbyn loyalists including Diane Abbott, Ian Lavery and the recently defeated MP for Durham North West, Laura Pidcock.

But Long-Bailey appears to hint that Rayner, the shadow education secretary, could have broader reach across the party, warning colleagues: “If there are people in our party who are more interested in beating the left than winning back power for Labour, we must ensure that we isolate them, not help them to isolate us.”

Despite giving Jeremy Corbyn a score of 10 out of 10 for leadership in a recent interview, Long-Bailey also warns colleagues against underestimating the challenges facing the party. “We know that our socialist policies are popular with the general public – policies like the Green Industrial Revolution, public ownership of water, energy, rail and mail all polled favourably.

“However, sadly, we weren’t trusted on Brexit, weren’t trusted on dealing with antisemitism, and all too often over the past four years looked divided as a party, particularly within the parliamentary Labour party,” she writes.

“We cannot pretend that these problems don’t exist and hope that they will disappear. It is only by being honest with ourselves and trying to understand the causes of these problems that we can tackle them and navigate a route back to power.”

Some longtime Corbyn allies are wary of Rayner, believing she is not sufficiently leftwing, but Long-Bailey – who is her friend and flatmate, as well as a political ally – describes her in the letter as “another fantastic working-class woman”, saying she trusts her.

Rayner has comfortably passed the threshold of nominations from MPs and MEPs to enable her to proceed to the next stage of the contest, with 72 so far, while Burgon, the MP for Leeds East, has 18 – just short of the 22 required.

A bloc of younger, leftwing MPs, including Lloyd Russell Moyle, Dan Carden and Alex Sobel have yet to declare, however.

A source from Rayner’s campaign said the letter showed that “Becky has the guts to face down the old guard”, and that “the new generation of the left are going to assert themselves in shaping the future of the Labour party”.