
The home secretary says the "incentives" will deliver a "significant saving to the taxpayer".
Mahmood unveiled the scheme as she sought make the "Labour case" for restricting support to some asylum seekers in a speech to a left-leaning think tank on Thursday.
The government already runs a voluntary returns programme, under which asylum seekers who choose to leave the UK can receive up to £3,000 in financial support.
Mahmood said housing a family of three in asylum accommodation costs up to £158,000 per year.
The home secretary said the UK government wanted to offer an "increased incentive payment" that will represent a "significant saving to the taxpayer", in an echo of reforms introduced in Denmark.
Mahmood said the government was consulting on how to remove families with children who refuse to leave voluntarily "in a way that is humane and effective".
She argued that not removing families had created "a perverse incentive" to cross the Channel with children.
Refugee and Migrant Children's Consortium, a coalition of 100 organisations, said families would have "just a week to make a potentially life-changing decision" without "time to access legal advice".
The group also raised concerns that cutting support for families would leave children homeless.
Conservative shadow home secretary Chris Philp said the payments were "an insult to the British taxpayer".
Reform UK has also suggested financial incentives for voluntary deportations, but the party's home affairs spokesman Zia Yusuf said £40,000 payments were "staggering" and "a prize for breaking in illegally".
A government source argued the payments would not encourage people to come to the UK illegally, saying smugglers charged between £15,000 and £35,000 per migrant, so it would cost more for someone to travel here.
Disclaimer
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