European Union leaders have repeatedly said that the United Kingdom can only stay in the single market if we continue to accept the free movement of people across Europe, which would stop the Government setting its own immigration policy.
Former finance minister George Osborne, who May sacked after taking office following the Brexit vote last June, said she was now a "dead woman walking".
Just more than a week away from the formal start of Brexit negotiations, British Prime Minister Theresa May is scrambling to cobble together a new government in Westminster - and to keep maintain her own position in 10 Downing Street.
As rumours swirled about plots to oust May, Johnson denied he was planning a leadership challenge.
Speaking to the "Sunday Mirror", Mr Corbyn said: "I can still be prime minister".
"The Labour left remembered that you don't win by tacking to an imaginary center - you win by letting people know you feel their anger and giving them a constructive end to channel it towards".
Labour leader Jeremy Corbyn, riding a wave of acclaim for his party's unexpectedly strong showing, called on May to resign.
"She's staying, for now", one Conservative Party source told Reuters. And if, as many publications claim, the generation gap is the largest political divide in modern Britain, young people simply can not fail to show up if they want a society that even vaguely resembles what they believe in.
Instead, voters stripped the Conservatives of their parliamentary majority.More news: Kickboxer Murthel Groenhart KO's Opponent, Gets Attacked By Fans in Ring
This is seen as a vote of confidence, and if it is not passed then the government will fall and Mr Corbyn will get his opportunity to form a government and purse his socialist policies in power.
Former minister Anna Soubry, who is fiercely pro-EU, insisted this morning that the PM must "absolutely" water down her Brexit plans.
"We can confirm that the Democratic Unionist Party have agreed to the principles of an outline agreement to support the Conservative government", a spokesman for May said.
"We all need to pull together to take on Theresa May and take on the Tories", she told Sky News.
Downing Street says it hopes to finalize the deal next week, after Parliament resumes sitting.
The very least which that support could involve would be a confidence and supply arrangement. That means the DUP will back the government on key votes, but it's not a coalition government or a broader pact.
The arrangement with the DUP will make governing easier, but it makes some Conservatives uneasy. The DUP is a socially conservative group that opposes abortion and same-sex marriage and had links to Protestant paramilitary groups during Ireland's sectarian "Troubles".
A deal between the government and the DUP could also unsettle the precarious balance between Northern Ireland's British loyalist and Irish nationalist parties. It is due to present its platform for the next session in the Queen's Speech at the State Opening of Parliament on June 19. The debate on the Queen's Speech usually lasts about five or six days.
She told BBC1's Sunday Politics: "The country did not vote for a hard Brexit".