Heidi Alexander thought to be considering role at London City Hall

Heidi Alexander, the former shadow health secretary, is considering quitting the Commons to accept a senior job at City Hall with London mayor Sadiq Khan, the Guardian understands.

Alexander was Khan’s campaign chair during the 2016 London mayoral election. The MP, who has spearheaded the campaign to keep the UK in the single market since leaving the shadow cabinet, currently represents Lewisham East.

It is understood Alexander may be considering taking a prominent role at City Hall under Khan, though no timeline was given for her departure. Khan’s spokesman declined to comment.

Alexander has been the co-chair, with Alison McGovern, of the Labour campaign for the single market, aimed at shifting the party leadership’s position on the issue.

Brexit has been her focus since the June election, where her majority increased by 11%. She has authored reports for the campaign group, coordinated Labour petitions and campaigned for parliamentary amendments and motions at Labour conference to advocate for a soft EU exit.

Alexander, who was elected in 2010, was previously full time deputy mayor for Lewisham, overseeing regeneration schemes.

However, since quitting the shadow cabinet in protest at Corbyn’s leadership in July 2016, Alexander has come under pressure from pro-Corbyn campaign group Momentum, including some local activists who are also members of the far left Alliance for Workers’ Liberty.

The influx of new members has sometimes represented a direct challenge, with local members vocally objecting to her decision to quit the shadow cabinet.

Momentum’s position is stronger in the neighbouring constituency of Lewisham Deptford; however, the campaign group last week launched a Lewisham East left caucus, to “help comrades build a strong left in the remaining stronghold of the Labour right in Lewisham”.

Should Alexander quit the Commons in order to take up the role, there is likely to be a fierce battle for her south London seat, which was retained at the last election with a majority of more than 21,000.

If Alexander is appointed by Khan, he would gain an experienced and popular Labour ally, bolstering his links with the parliamentary party ahead of his re-selection later this summer. Claire Kober, the outgoing leader of Haringey council, has also been recently linked with a job with Khan at City Hall after May’s local elections.