According to excerpts from May's speech, cited by Reuters, EU nationals “will no longer be able to jump the queue after Brexit” noting that the UK system will be focused on business and “will have more streamlined application and entry processes”.
Earlier on Sunday, May said that toppling her as British PM would risk delaying Brexit and she would not let talk of a leadership challenge distract her from a critical week of negotiations with Brussels.
“These next seven days are going to be critical, they are about the future of this country," May told Sky News. "I am not going to be distracted from the important job".
“Some politicians get so embroiled in the intricacies of their argument they forget it is not about this theory or that theory or does it make me look good,” she noted in an interview for the Daily Mail published this Saturday.
May observed that political opponents inside the party think too much of what they consider to be her privileged position and too little about the responsibility that accompanies that privilege.
“The job of a prime minister is to make tough decisions which are not always black or white. I have to find a way through, what best suits everybody's needs,” May said, noting that she admits that her Brexit plan is “not everybody’s ideal deal.”
She also noted that she was surprised that so little attention has been paid to a fulfilment of the 2016 Referendum promise – the end of the freedom of movement and the beginning of the controlled immigration.
“As Home Secretary for six years, I did my best to reduce immigration with one hand tied behind my back because you couldn't do anything about people coming in from the EU. Now we can. Freedom of movement ends,” she declared.
Meanwhile, former Foreign Secretary Boris Johnson wrote in his weekly column for Monday's Daily Telegraph that May’s suggestion that the issues with the Brexit draft agreement can be dealt with in future talks is 'a tragic illusion' and 'an attempt at deception'.
"Of all the lies that are currently being peddled, the worst is that this agreement can somehow be remedied in the next stage of the talks. I have heard it said that this is like a football match, in which we are one-nil down at half-time, but as the Prime Minister suggested in her interview… we can still pull it back and get the Brexit we want," Johnson said.
He also added that he is 'afraid' since “we [the UK] are about to give the EU the right to veto our departure from the customs union. Why should they let us go?”
Johnson, who resigned in protest over May’s Brexit plans in July, has been pegged as one of the current prime minister's potential successors if Conservative Party members are able to submit enough letters of no confidence to start voting on May’s position as party leader.
Johnson also said that Britain should scrap the so-called Northern Ireland backstop, an insurance policy to avoid a return to border checks between the British province and EU-member Ireland in order to avoid 'economic and political servitude' to the EU.
He suggested that both sides should discuss new, unobtrusive checks away from the frontier. He also suggested Britain should withhold at least half of the 39 billion-pound divorce payment until an enhanced Canada-style free trade deal between the EU and the UK is reached.
“This needs to be treated as a challenge to be overcome, not as an inevitable disaster; because after the short-term logistical difficulties, the prospects for jobs and growth, and free-trade deals, would be very good indeed,” he said.
On Saturday, five pro-Brexit senior Conservatives, including House of Commons leader Andrea Leadsom, had reportedly attempted to persuade May to renegotiate the Brexit treaty.
The current draft deal is under review by the 27 EU member nations. Following that, the exit treaty will require approval from the UK Parliament to ratify the legalities of the withdrawal.