The British Government has apologised for its "appalling" treatment of some immigrants from the Caribbean, as reports of people being threatened with deportation overshadowed a Commonwealth leaders' meeting.

Britain wants to use this week's summit of the alliance of the UK and its former colonies to help Britain bolster trade and diplomatic ties around the world after it leaves the European Union.

But anger over what many see as the UK's shabby treatment of residents of Caribbean origin eclipsed trade topics.

Members of the "Windrush generation" — named after the ship Empire Windrush, which brought the first big group of postwar Caribbean immigrants to Britain in 1948 — came from what were then British colonies or newly independent states.

Those who arrived before 1971 had an automatic right to settle in the UK.

But some from that generation, especially those who arrived as children on their parents' passports, say they have been denied medical treatment or threatened with deportation because they can't produce papers to prove their status.

Britain's Home Secretary Amber Rudd has promised no one will be deported. ( Reuters: Hannah Mckay )

The Guardian newspaper reported on the mistreatment of people such as former House of Commons cook Paulette Wilson, who moved to Britain at age 10.

She was sent to an immigration detention centre last year after failing to convince authorities she had the right to remain in Britain.

British Labour Party MP David Lammy demanded answers from the government on Monday, calling it "a day of national shame".

British Home Secretary Amber Rudd said she was setting up a task force to sort out the Caribbean immigrants' paperwork simply and for free, and promised no one would be deported.

"We have seen the individual stories, and they have been, some of them, terrible to hear, and that is why I have acted," Ms Rudd said.

"Frankly, some of the ways they have been treated has been wrong, has been appalling and I am sorry," she said.

British Prime Minister Theresa May's office said she would meet with her Caribbean counterparts at the Commonwealth summit to discuss the situation.

UK getting tougher on immigration

The British Government has taken an increasingly tough line on immigration, which has increased dramatically over the last 10 or 15 years, largely as a result of people moving to the UK from other EU countries.

A desire to control immigration was a major factor for many voters who supported the 2016 referendum for Britain to leave the EU.

Critics say the government has, by design or accidentally, taken a hostile attitude to the thousands of people who have made Britain their home.

Barbados High Commissioner Guy Hewitt told the BBC he felt Britain was telling people from the Caribbean: "You are no longer welcome."

Some 140 UK politicians signed a letter urging the government to find an "immediate and effective" response to concerns from Commonwealth-born residents over their immigration status.

AP