In a tweet accompanying the article, the Home Office said Nokes "dispels the myth that this government is clamping down on Commonwealth citizens".
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".
It has seen some Windrush generation residents, who might never have applied for United Kingdom passports, left without the documentation now required by officials.
Interior minister Amber Rudd is set to announce a team to ensure no one will lose services or entitlements, and that if people apply for new documents, the usual fees will be waived, the BBC reported.
"I do not want of any of the Commonwealth citizens who are here legally to be impacted in the way they have and, frankly, some of the way they have been treated has been wrong, has been appalling, and I am sorry", Rudd told parliament.
There is widespread anger that long-term British residents have fallen victim to rule changes in 2012 - when May herself was interior minister - aimed at stopping overstaying.
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.
The Home Secretary said high commissioners would have an opportunity to raise any such cases with her at their meeting later this week.
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The name comes from the Empire Windrush, the ship that brought the first large group of post-war West Indian immigrants to the United Kingdom carrying 492 passengers on a voyage from Jamaica to London in 1948. Ministers have said they hope to tighten ties and increase trade with the Commonwealth, a network of 53 countries, mostly former British colonies, after Britain leaves the European Union next year.
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".
British media have reported cases such as a man who was denied treatment for cancer and a special needs teaching assistant who lost his job after being accused of being illegal immigrants despite living in Britain for more than 40 years.
More than 140 MPs from all parties have signed a letter to Theresa May expressing concern over the so-called Windrush generation.
The Home Office's renewed guidance, published last week, offers no security or certainty.
May only became aware of a request for a meeting on Monday morning, and will discuss the issue with counterparts from Caribbean nations this week, her spokesman said.
Her comments came as the Prime Minister's official spokesman said the PM was clear that nobody with a right to be in the United Kingdom would be made to leave.
The Tottenham MP said it was a "national shame" that it had taken so long for the government to speak on the issue, calling it "inhumane and cruel" for those who waited for them to act.