Jeremy Corbyn has accused Theresa May of abandoning the UK’s moral duty to protect refugees following threats by the contractor Serco to evict asylum seekers in Glasgow.

The Labour leader is to meet some of the families affected by Serco’s decision to evict up to 330 refugees in Glasgow, starting with at least 18 asylum seekers this month – many of whom are fighting Home Office deportation orders.

In a statement in advance of his visit on Wednesday, Corbyn said: “Asylum seekers who have fled horrific conflict and violence and have since made the UK their home deserve our help and support, not persecution from profiteering private companies.

“[Theresa] May’s government has failed to uphold our country’s moral duty to refugees. Labour will end the Tories’ ‘hostile environment’ policy that has caused such cruel and inhumane treatment of British citizens as well as asylum seekers and refugees.”

The lock-outs were temporarily halted after protests in early August which led to the Home Office immigration minister, Caroline Nokes, calling urgent meetings with the Scottish communities secretary, Aileen Campbell, and Glasgow council leaders.

The housing charity Shelter is applying for a court order on 27 August to lift the threat of eviction for two people still pursuing asylum. It accuses the Home Office of breaching their human rights.

Govan Law Centre, a public interest law firm specialising in housing, has begun legal action in the court of session in Edinburgh to test the legal basis for the policy as a whole. Activists say this case has implications for similar evictions in England.

Serco claims it has provided free accommodation for months to some asylum seekers even after their application has been rejected by the Home Office. The Home Office insists no-one will be left destitute.

Labour hopes the controversy will give Corbyn a chance to champion a popular Scottish human rights cause, and boost his image. The party’s support in Scotland has slipped back to put it third behind the Tories after its surge in popularity in last year’s snap general election proved short-lived.

Labour claims that Nicola Sturgeon, the first minister, has had little direct involvement in this issue even though some of those affected live in her Glasgow Southside constituency.

But Sturgeon attacked the Home Office when the case erupted in early August, describing the evictions policy as unacceptable. The Scottish government has given the destitute asylum seeker service, run by the Scottish Refugee Council and other charities, £110,000 in emergency funding to support those affected.

“It’s a responsibility for those of us in rich countries to provide refuge. One of the marks of a civilised society is how we deal with the most vulnerable in society,” she said.