The Home Secretary told MPs she did not know about migrant removal targets.
A former border chief has said Amber Rudd’s claim to have not known about immigration removal targets was “disingenuous”.
Documents setting out performance reports, bids for Government cash and departmental plans include targets set by services, according to Rob Whiteman.
Ms Rudd has faced repeated calls to resign amid claims that her department is “out of control”.
Mr Whiteman, chief executive of the UK Border Agency from 2011 to 2013, told BBC Radio 4’s Today programme: “There are targets. All public services, whether immigration or education or hospitals or the criminal justice system, operate on targets in order that staff can know what’s expected to happen in a particular year.”
He added: “Targets are set operationally by managers but, of course, ministers would know there are targets. They are intelligent people and they will see performance reports, bids to Treasury for resources, the departmental plan which would cover the targets that are being set for individual services.
“Fair’s fair, ministers could say we don’t actually set these targets, they are being set by the operations but I think it is disingenuous, surely, to suggest that they don’t know that they exist because they will have seen them in performance reports and other internal documents.”
The Home Secretary denied on Wednesday that targets were used as she was quizzed by a Commons committee probing the Windrush scandal.
But her comments were at odds with a 2015 inspection report which said the practice did exist.
On Thursday, Ms Rudd said she never agreed to use removal targets for migrants, adding that those used by her department “were not published targets against which performance was assessed”.
The Cabinet minster also ordered the director general of Immigration Enforcement to direct local teams to stop using targets.
At a lunch with journalists in Westminster she admitted she was fighting for her political career, telling the gathering she was “just thinking about staying in the game”.
Labour leader Jeremy Corbyn has led calls for Ms Rudd to quit.
But Labour former Home Secretary Lord Blunkett said he did not consider the row a resignation matter.
He told Today: “On this occasion it would appear, and I like her a lot and I don’t think she should resign because I don’t think it is a resigning matter, but I would like to know from Amber Rudd whether she did her homework, because it is pretty basic stuff when you appear in Parliament or in front of a select committee to be able to answer the questions.”
The Labour peer said “imbalancing” the Brexit balance in the Cabinet “would not be in the best interests of the country”.
“I think she needs to get her act together,” he added.
“On a purely party political old-style jungle fight, if I thought this would actually change the government then I might consider it, but actually I don’t believe it would.
“I think it would be damaging to those of us who want at least some sane voices inside the Cabinet.”
MPs are to debate a petition calling for an amnesty for the Windrush generation which was signed by more than 177,000 people.
The Commons Petition Committee announced that a debate on the call for an amnesty “for anyone who was a minor that arrived in Britain between 1948 to 1971” along with Government compensation for “loss and hurt” will be held on April 30 in Westminster Hall.