Shabana Mahmood said she is considering “a big increase” in payments for migrants to return voluntarily to their home countries.

Under current rules, the UK offers payments of up to £3,000 for some people with no right to remain in the country to return home.

The Home Secretary has directed officials to “pilot a small programme” of increased payments, “just to see how it changes behaviour”.

The Birmingham Ladywood MP has insisted the policy represents “value for money” but admitted it “sticks in the craw” for Britain’s hard-pressed taxpayers.

In plans to overhaul the asylum system set out on Monday, Ms Mahmood said the offer of financial packages to assist with voluntary returns would continue.

But she has now said the figures involved could increase.

She told the BBC’s Political Thinking podcast: “I haven’t alighted on the full sums involved yet, but I am willing to consider a big increase on what we currently pay.

“I know it sticks in the craw of many people and they don’t like it, but it is value for money, it does work, and a voluntary return is often the very best way to get people to return to their home country as quickly as possible.”

Downing Street has defended the plan for increased payments, saying: “We make no apology for saving taxpayers millions of pounds by removing individuals who have no legal right to remain in the UK, or who are seeking to leave voluntarily.

“You’ll have seen already, the Government has increased removals, almost 50,000 people removed, including around 5,200 foreign national offenders.

“For example, to use a specific case, the £500 spent to remove Hadush Kebatu that you’ll remember was, of course, uncomfortable, but it would have cost thousands to get him out on another flight.

“So, payments for voluntary returns play a vital role in this, helping to curtail lengthy legal challenges to removal that cost the taxpayer millions of pounds.”

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The Home Secretary’s asylum system reforms include scrapping guaranteed housing and weekly allowances for asylum seekers and those who can work or have valuable assets will have to contribute to their costs in the UK.

Under the proposals, families with children could also be subject to enforced returns under measures to remove those with no right to be in the UK.

Refugees will meanwhile have to spend 20 years in the UK before being allowed to apply for settled status, up four times from the current five years.

Labour backbenchers have strongly criticised Ms Mahmood’s wide-ranging reforms, which are aimed at deterring migrants from seeking asylum in the UK and making it easier to remove people with no right to be in the country.

Former Labour frontbencher Richard Burgon said the policy “scrapes the bottom of the barrel” and was “a desperate attempt to triangulate with Reform”.

Labour mayor of Greater Manchester, Andy Burnham, today voiced “concerns” about the plans, saying they could leave people “unable to integrate”.

He told BBC Radio 4’s Today programme: “I agree that Shabana Mahmood is right to grasp this nettle and have root-and-branch reform of the system.

“I agree with that, but I do have a concern about leaving people without the ability to settle.

“One of the concerns being that if there’s a need to constantly check up on the status of countries where people have come from, that might limit the ability of the Home Office to deal with the backlog.

“And it also may leave people in a sense of limbo and unable to integrate.”

Education Secretary Bridget Phillipson insisted the asylum system will be “fair”.

She said: “Our country has always been open, tolerant and outward looking, but if we want to maintain public confidence in the immigration and asylum system, then it’s right we take action.

“We’ve responded to what people have been telling us, but it will be a fair system, but a system with a clear set of rules and rules that will be enforced.”