Unite and Momentum are expected to back rival candidates for the battle to become Lewisham East’s next Labour MP, the Guardian has learned.

Momentum’s national coordinating group is likely to back Lewisham councillor Sakina Sheikh, a former student campaigner who has close links with the grassroots group. Unite has already formally backed Islington councillor Claudia Webbe, a member of Labour’s national executive committee (NEC) and a former adviser to Ken Livingstone.

A Momentum source suggested the group wanted to back a candidate with local credentials. “The local Momentum heavily backs Sakina and it feels like she will get the national backing, as they are keen to make sure it’s a local candidate with the endorsement of local members,” the source said.

However, Lewisham Momentum itself is split, with a recent AGM ending in a dispute. A Facebook post on the group’s account on Tuesday shared details of a campaign phone bank for Webbe.

Unite announced on Tuesday it was backing Webbe, the more experienced candidate, saying she would be “a huge asset in parliament”. The trade union said Webbe was “a lifelong socialist who tirelessly fights the corner of working people, and for justice for those let down by our political system”.

Two other candidates have also been shortlisted, councillor Brenda Dacres, who stood unsuccessfully to be Lewisham mayor earlier this year, and Janet Daby, Lewisham’s deputy mayor. Lewisham East’s local party is controlled by party centrists, who are likely to organise for Daby or Dacres. A Momentum source said the seat could be “a real tough battle” for the left in the local party.

The final selection hustings for the seat, which has a 21,000 Labour majority, will take place on Saturday, when party members will vote for their preferred candidate to fight the by-election in June. The process was slowed down following an email campaign by grassroots party members who felt the initial timetable was too rushed.

Ian McKenzie, the chair of Lewisham East CLP, said: “I’m absolutely delighted that the NEC has listened to local members and given us a say on who is on the shortlist, so members have a genuine choice. It looks like Jeremy Corbyn’s member-led democracy actually means something.”

Two of the four shortlisted candidates, Daby and Dacres, were on a list published unilaterally by the local party, but which has no formal role in drawing up the shortlist. Centrist activists in Lewisham had feared the NEC, on which Corbyn’s backers now have a majority, would only allow them to choose between candidates from the left wing of the party.

The byelection was called after the resignation of Heidi Alexander, the former shadow health secretary, who quit to take up a role as deputy mayor for transport under the mayor of London, Sadiq Khan, at City Hall. Alexander has been co-chair of the Labour campaign for the single market.

Corbyn paid tribute to her at a meeting of the parliamentary Labour party in Westminster on Tuesday night. A Labour source said Corbyn had joked that he would lobby Alexander in her new role for a new bus stop in his Islington North constituency.