Between the 1920s and the 1970s, 130,000 children were sent to former British colonies, mainly Canada and Australia.

The children, most of whom came from deprived backgrounds, often faced difficult lives of hard labour and servitude in their foster homes.

Many were physically and sexually abused and were often separated from siblings.

In 2010, then Prime Minister Gordon Brown apologised, saying he was sorry children “were allowed to be sent away at the time when they were most vulnerable”. The Australian government apologised in 2009 for the cruelty shown to the child migrants.

Rex Wade was sent from Cornwall to Tasmania at the age of 10, where he was treated “cruelly for any misdemeanour”, with those in charge setting a dog on the children when they misbehaved.

He told the BBC last year: “It was physical, verbal and mental abuse. I lost everything I ever had; the relationships I had with my family. It’s a lot to deal with and you just don’t get over it.”

In a letter seen by The Guardian, the government said it would pay former child migrants £20,000.

“The claimant must have been sent by a church, state, voluntary or other organisation … and must not have been accompanied by an adult family member, or sent to live with a member of their birth family,” the government said in the letter announcing the decision.

It added: “The government has long acknowledged and accepted that assessment at the time of the national apology in 2010 and in fact went further, calling it a ‘shameful episode of history and this failure in the first duty of a nation, which is to protect its children’.”

The Child Migrants Trust will accept applications from 1 March 2019 and will remain open for two years. Claims made thereafter will be considered on a case by case basis.

A Department of Health and Social Care spokesperson said: “The government is working closely with the Child Migrants Trust to develop and establish the payment scheme and the Trust will start accepting applications from 1 March 2019.”