The government has announced a hardship fund to provide up to £5,000 to members of the Windrush generation who were wrongly targeted by the hostile environment policy and left destitute, following months of pressure from MPs and campaigners.

The Home Office published guidance on Monday with information on who would qualify for the fund, calling on members of the Windrush generation in urgent financial need, who could not wait for the Windrush compensation scheme, to get in touch.

For a case to be considered, the person applying has to be part of the Windrush cohort and to provide a compelling reason why they cannot wait for the full compensation scheme. The fund will be used to support the claimant’s life, dignity or ability to return to the UK in an urgent circumstance.

The Home Office will also consider whether the claimant has previously been denied entry to the UK and whether they have access to alternative funds.

In a letter to the home affairs committee, the home secretary, Sajid Javid, said: “I acknowledged that there may be some urgent and exceptional cases where it is right to consider whether individual circumstances warrant a payment to be made before the compensation scheme is in place. That policy, setting out the approach and decision-making process in these cases, has now been published.”

Satbir Singh, the chief executive of the Joint Council for the Welfare of Immigrants, welcomed the announcement but said the charity was “deeply troubled” that the Home Office had said any money given out might count against future claims.

He added: “It is misleading for the government to suggest that this is in any way ‘immediate’ support, as the published timeframes suggest that the first payments will not be made well into the new year. It’s disappointing that after his department has ruined so many lives, the home secretary, Sajid Javid, is still trying to get away with doing the bare minimum to respond to this crisis.”

The Labour MP David Lammy, who has been calling for a hardship fund since the scandal broke in April, said: “This Christmas, many Windrush citizens and their families will be in poverty as a direct result of appalling mistreatment by their own government. It is both disrespectful and shocking that it has taken the home secretary nine months to set up a hardship fund given this is something I and others have been calling for ever since this scandal broke last Easter.

“Trust in the government is low in the black community for very good reason. We are still without a full compensation scheme, and this announcement appears to have been cynically made on a heavy news day when many members of the Windrush generation may well be totally unaware of it.”

Hubert Howard, who arrived in the UK with his mother aged three in 1960, lost his job and was denied benefits after the Home Office classified him as an illegal immigrant. He welcomed news of the hardship fund, saying he knew many who desperately needed it. But he said he was disappointed by the lack of progress on the compensation scheme.

“I’ve been to all the meetings. I’m very disappointed. They’ve come out with nothing at all. All they’re asking about is stories. I don’t like talking about my story. When I think about my mum, tears come out of my eyes. I don’t really like to talk about it all,” he said. Howard was unable to travel to visit his mother in Jamaica before she died.

“I just don’t know what’s going on,” he said. “There’s nothing at all that has come out of it. Every time I go there, that’s all they want to know – stories, stories stories. I’m tired of stories. They need to move to action.”

Another victim of the Windrush scandal, who was prevented from returning home to the UK for 13 years, told MPs he had received no apology or help from the government since his return in September.

Vernon Vanriel, a former boxer who had lived in London for 43 years until his re-entry was barred in 2005, told the public accounts committee that the Home Office had offered him no assistance in seeking housing and no acknowledgement that he should have been allowed to return sooner.

Vanriel told MPs that he lost his secured tenancy and his work as an electrician after leaving the UK and had returned to live in his sister’s home and receive limited benefits. After he sought help from UK authorities the government paid for his flight, but he had not been approached by anyone offering any additional assistance since, he said.

A Home Office official, Diana Luchford, told the hearing she believed there had been offers of help to Vanriel, but she would examine his claims.