The news is a U-turn for the Prime Minister after she refused a formal diplomatic request to discuss concerns leaders have for scores of long-term British residents incorrectly deemed illegal immigrants.
Many have never applied for a passport in their own name or had their immigration status formalised, as they regarded themselves as British.
The Home Office earlier confirmed the meeting was requested but the subject of the proposed meeting was not made clear.
Mrs May is to meet her counterparts from Caribbean states in the margins of the Commonwealth summit in London on Tuesday amid growing anger about individuals facing the threat of deportation and being denied access to healthcare due to United Kingdom paperwork issues.
"I don't know the numbers, but what I am determined to do going forward is to say we will have no more of this".
May's official spokesman said: "She deeply values the contribution made by these and all Commonwealth citizens who have made a life in the United Kingdom, and is making sure the Home Office is offering the correct solution for individual situations".
The PM's spokesman said the Home Office was expected to set out measures to support members of the Windrush generation in providing the documentation necessary to prove their right to live in the UK.
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The letter to Mrs May calls for action over the immigration anomalies, stating: "All too often these routine bureaucratic errors bring about the separation of families and irreparable damage to lives in addition to undue stress, anxiety and suffering".
The descendants of Britain's first wave of immigrants from its Caribbean former colonies are facing losing jobs and even deportation despite living and working in the United Kingdom for decades in a controversy which threatens to overshadow a meeting of the leaders of the Commonwealth of Britain and its former colonial possessions.
Labour MP David Lammy had co-ordinated a letter to the PM condemning the "grotesque, immoral and inhumane" situation. It is a stain on our nation's conscience and the Prime Minister must act urgently to right this historic wrong. "Those are the people we are working hard to help now".
"The government is essentially stripping people of the rights that our government itself granted decades ago".
The Immigration Minister added: "These are people who we welcomed here way back in the '50s and '60s and it's really important to me that we correct any error". Admitting some "horrendous situations", immigration minister Caroline Nokes told BBC Radio the government had "an absolute responsibility to make sure there are no more of these mistakes".
It said: "We urge you to guarantee the status of all Commonwealth nationals whose right to remain is protected by law and to provide an effective, humane route to the clarification of their status".
Mr Hewitt, Barbados high commissioner, told the BBC: "I have held as a great honour the fact that I am the first London-born high commissioner for Barbados".
"They thought that there was no need for them to regularise their status".