Up to 21,000 asylum seekers who have waited for a year for their claims to be processed could be allowed to enter the jobs market so they can support themselves, the Home Office has said, as part of a package of measures to be announced on Thursday.

As the government seeks to empty asylum hotels, claimants who break the law, work illegally or are found to have enough assets to live without support will from June be ejected and lose their support payments.

The developments have been questioned by the Refugee Council for risking an increase in rough sleeping among those escaping war and famine.

They come as Shabana Mahmood has hit back in a column for the Guardian at demands from senior labour movement figures for ministers to stop focusing on migration and to soften their attacks on the Green party.

The home secretary wrote: “Restoring order at our border is not just an embodiment of Labour values, it is the necessary condition for a Labour government to do anything at all.”

Mahmood wrote that Labour’s vision should appeal to the mainstream and be “neither the nightmare of Farage’s borders, effectively closed, nor the Greens’ fairytale of borders effectively open”. She also said the government planned to launch a new “safe and legal” route in the autumn for students seeking refuge.

There are about 30,600 people awaiting asylum claims living in roughly 200 hotels across the UK, and 107,000 people receiving asylum support, the Home Office said.

At present, those in dispersal accommodation, such as private housing, receive £48 a week, while those in hotels receive £9.95 per person.

Officials are seeking to move on many of the 21,000 people who have been in hotels for more than a year by extending permission to work.

If they find work, the intention is that they would fall under the category of having asylum support removed and eventually move out.

The statutory legal duty under EU law to provide asylum seekers with support and accommodation would be revoked on Thursday, the Home Office said.

Instead, it would be replaced with a conditional approach, so support would be reserved only for those who genuinely needed it and followed the law.

The measures, that will be laid in parliament and come into force in June, would remove support payments and accommodation to asylum seekers who illegally work, have the ability to support themselves, have the right to work or have broken the law.

The Home Office did not respond to questions asking if the 21,000 would be restricted to jobs on the “immigration salary list”.

Asked on what criteria the Home Office would decide whether an individual has enough assets to survive without financial support, a source said it would be “on a case by case basis” and with no set threshold.

Keir Starmer and Mahmood have been facing calls from across the labour movement to move towards progressive policies in the wake of the Green party victory at the Gorton and Denton byelection.

Sadiq Khan, the mayor of London, wrote in the Guardian: “A political strategy of taking liberal, progressive voters for granted is clearly flawed.”

“The vast majority of those who are thinking of voting Green are not extreme,” Khan said.

The latest announcement comes after the home secretary visited Denmark last week to see how it has tackled immigration, bringing asylum claims to a 40-year low.

Mahmood is following the Danish model in which the government seeks to make it less attractive for illegal migrants to come to the UK.

She will make a speech today at the IPPR thinktank on Thursday outlining how these reforms are in line with her British values.

Imran Hussain, the director of external affairs at the Refugee Council, said: “Forcing people into destitution will not fix the system or deter people who have escaped torture or persecution. Instead, it is more likely to push them into sleeping rough, and shift costs on to local authorities and the NHS, making cases harder to resolve.”