A "handful" of people have been wrongly deported from the UK since 2012, the country's most senior immigration enforcement official has admitted.
Hugh Ind told MPs "up to five" people had been brought back to the UK after their removal was called into question.
Ministers have repeatedly said they are not aware of any deportations of Windrush settlers or their families amid the controversy over their status.
Mr Ind also conceded there was a "deep problem" with wrongful detentions.
Critics of the government's "hostile environment" policy towards illegal migration claim it has led to the detention of people living legally in the UK, in particular relatives of the Windrush generation which came to the UK from the Caribbean after World War Two.
A row over immigration removal targets and the government's handling of the Windrush controversy led to Home Secretary's Amber Rudd's resignation last month.
At a meeting of the Home Affairs Select Committee on Tuesday, the Home Office's most senior official Sir Philip Rutnam said there had been targets for removing immigration offenders in each of the past three years.
In the days before she quit, Ms Rudd told MPs on the same committee there were no targets, a fact that was subsequently contradicted by official memos, and then argued that she had not been aware of them.
Sir Philip apologised for what he said was the "regrettable confusion" over the issue at the previous hearing but rejected suggestions that Home Office officials accompanying Ms Rudd had "lied" to MPs.
He said he was launching a review of the advice Ms Rudd was given by civil servants in the run-up to and during the hearing that preceded her exit and he hoped that the prime minister's adviser on standards, Sir Alex Allen, would provide a "definitive account" of what had happened.
Sir Philip told MPs there were no national removal targets in 2018-19, after it had been decided in the last few months of 2017-18 that the word "target" wouldn't be used.
But he said there remained what he described as an "expectation" that those people who had no right to be in the UK would be pursued.
During angry exchanges with the Labour MP Stephen Doughty, Sir Philip rejected an accusation that he was using "slippery tactics" by using different terms to describe targets.
Pressed by Mr Doughty whether anyone had been wrongfully deported in the past six years, Mr Ind - who is director general of immigration enforcement - said yes.
He added: "There have been times when we have brought individuals back... I'm thinking of a handful."
Asked to be more precise, he said he believed there were "up to five" cases since 2012.
Earlier during the hearing, Immigration Minister Caroline Nokes said she did not think she had had "any cases of wrongful deportation brought to my attention, no".
Asked why the minister was not aware of the cases he himself had spoken of, Mr Ind said: "I don't know."
Mr Ind also suggested some local enforcement teams, including those removing foreign national offenders, were retaining the ability to set local removal targets this year.