Photo taken on Jan. 29, 2016 shows the UK and EU flags outside the European Commission headquarters in Brussels, Belgium. [file photo: Xinhua/Ye Pingfan]

Britain's Brexit minister indicated on Sunday that European Union (EU) nationals who came to the country during the Brexit negotiations to leave the bloc might be not allowed to stay.

David Davis, who was appointed by new Prime Minister Theresa May to oversee the negotiations on Britain's exit from the 28-nation bloc, told Sky News during an interview that the EU migrants already in the country would not have to leave, but for newcomers, the government was likely to set a cut-off date.

"I want to see a generous settlement for the people here," he said, but if a large number of migrants arrive in the country before it leaves the EU, "we may have to say that the right to indefinite leave to remain protection only applies before a certain date," he spoke to The Mail on Sunday.

"You have to make those judgements on reality, not speculation," he added.

Border control was a key theme in the June 23 referendum in which around 52 percent of voters chose to leave the EU. According to the bloc's rules, EU citizens can move freely among member states, which led to a surge of immigration in Britain during recent years.

May, leader of the Conservative Party and elected as prime minister after the resignation of David Cameroon, has been criticized for refusing to guarantee the rights of the EU citizens in Britain.

As a response, she said she needed to ensure that hundreds of thousands of Britons living in the European continent get the same protection.

Under the Brexit timetable of Davis, the country would start the process of leaving the EU by the end of this year, after consulting with administrations in Scotland, Wales and Northern Ireland and other business groups and unions.