The comment will pile pressure on the prime minister to explain to MPs why she did not intervene, to point out that Amber Rudd – when denying the targets existed – had misled parliament.
Earlier, Chris Grayling, the transport secretary, suggested Ms May had been ignorant of the targets, because “an extensive period” had passed since she was home secretary.
But, in a TV interview, she said: “When I was home secretary, yes, there were targets in terms of removing people from the country who were here illegally.
“This is important. If you talk to members of the public, they want to be reassured that we are dealing with people who are here illegally.”
The revelation will sharpen the focus on the role of the prime minister, the architect of the “hostile environment” policy that ended up persecuting the Windrush generation.
Crucially, it is believed that any members of the Windrush generation detained for deportation – or prevented from returning to the UK – would have counted towards the now-revealed forced removal target.
Jeremy Corbyn said: “Amber Rudd has been a human shield for Theresa May – and now she has gone.
“Theresa May now has questions to answer about what she actually did as home secretary. She was presiding over, in her terms, the creation of a hostile environment.”
However, the prime minister’s spokesman said she no longer received internal briefings about the details of home office targets after leaving the post, in 2016.
In the interview, Ms May also rejected suggestions that the departed home secretary had paid the price for her earlier policy decisions.
“Amber Rudd was very clear about the reasons why she has resigned – that was because of information she gave to the House of Commons which was not correct,” the prime minister insisted.
“If you look at what we’re doing as a government, and have been doing over the years as a government, what we are doing is responding to the need that people see for a government to deal with illegal immigration. That’s exactly what we are doing.”
Ms May said the Windrush generation had been “caught up in way that has caused anxiety”, but were now receiving help to secure the documents they needed.
“We deal with that, we make sure that people are given the reassurance that they need, but we also need to ensure that we’re dealing with illegal immigration.” she vowed.
The prime minister, on a visit to the Labour target borough of Trafford, also sought to scotch Conservative fears that the Windrush debacle will damage the party in Thursday’s local elections.
“I think when people go to the polls on Thursday they will be asking [themselves] who do they want to see as their local councillors, who do they want to see running their local councils and when they do that they will ask themselves who is going to provide good services, who is going to keep council tax low?”
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies