A 2015 report says the Home Office set targets for voluntary departures of people who could not lawfully stay in the UK, it has emerged.
A powerful Commons committee investigating failures that affected the Windrush generation asked Home Secretary Amber Rudd whether her department has targets for migrant removals during a grilling on Wednesday.
Ms Rudd, who took over from Theresa May as Home Secretary in July 2016, told the Commons Home Affairs Committee she was not familiar with suggestions that regional targets were in place.
An inspection of removals by the borders and immigration watchdog said targets were set in 2014/15 and for 2015/16, which were then split between 19 Immigration Compliance and Enforcement (ICE) teams across the UK.
The targets, and how they were divided up, were first reported by the BBC.
Following Ms Rudd's appearance before MPs on Wednesday, the Home Office said it had "never been (its) policy to take decisions arbitrarily to meet a target".
Yvette Cooper, who chairs the committee, said the response was a "complete fudge" and she would be writing to Ms Rudd "to get a proper answer" on Thursday.
Jeremy Corbyn has called on Ms Rudd to resign over the Windrush scandal, claiming she had inherited a "failing policy" and made it "worse".
An outcry over treatment of migrants from the Caribbean who arrived after the Second World War has put immigration policy and its administration in the spotlight.
Ms Cooper said she had asked the Home Office whether it has targets for immigration removals after "contradictory evidence" from the Home Secretary and the Immigration Services Union.
A December 2015 report by the Independent Chief Inspector of Borders and Immigration says that targets were set for voluntary departures, which took place when an individual or family notified authorities of their intention to leave the UK.
Voluntary departures included people who had approached the Home Office for financial assistance with their travel arrangements.
The assistance was available to anyone over 18 who was in the UK illegally, had been refused leave to remain in the UK or had applied for an extension of leave but wanted to withdraw the application and depart.
The report said: "For 2014/15 (10 full months) the Home Office set a target of 7,200 voluntary departures, an average of 120 per week, with the weekly target rising to 160 by the end of March 2015.
"For 2015/16, the annual target was raised to 12,000. These targets were split between the 19 ICE teams across the UK."
The Home Office also had a process for returning families who had no legal right to remain in the UK, which had a "single numerical target".
The report said the target was "not a useful performance measure" due to the varying nature of cases year to year.