EU citizens might not be entirely free to reside in the country as work permits will be required.
UK's remaining candidates to lead the conservative party and eventually succeed PM David Cameron, both said they will impose harsher rules on EU citizens who want to work and live in Britain.
In separate interviews published on Friday, Home Secretary Theresa May and Energy Minister Andrea Leadsom said that limitations will be imposed in the free movement of EU citizens coming into Britain.
"People going on holiday or travelling on business or to collaborate on science will be able to do that but the right to reside and the right to work here will be under work permits," Andrea Leadsom told The Times newspaper.
She also suggested that everyone arriving after September 9 would not be fully protected by EU laws if they reside in the country.
"Under free movement you don't have to guarantee free movement for ever," she said.
Theresa May also referred to migration policies focusing mainly on free movement in the country.
"If I am prime minister, we will come out of the European Union and part of that will be control of free movement," she said during an interview with The Daily Telegraph newspaper.
A survey by ORB conducted for The Independent newspaper showed that 48 percent of voters prefer UK to have full access to the European Union single market while 37 percent said capping immigration from Europe is more important.
In her interview with The Times newspaper, Leadsom mentioned the fact that May does not have children saying: "She possibly has nieces, nephews, lots of people, but I have children who are going to have children who will directly be a part of what happens next."
The newspaper headlined the interview: "Being a mother gives me edge on May". Leadsom took to twitter to express her disappointment over the headline.
Truly appalling and the exact opposite of what I said. I am disgusted. https://t.co/DPFzjNmKie— Andrea Leadsom MP (@andrealeadsom) July 8, 2016