Mr Johnson set out his personal manifesto for Brexit in a 4,000 word article in the Daily Telegraph, which he did not inform Mrs May about until it was published.
The Foreign Secretary angered the Prime Minister when he said Britain should refuse to pay the European Union a big divorce bill.
His bold piece, which has caused anger across his party, was called ‘My vision for a bold, thriving Britain enabled by Brexit’.
Fellow Conservative Cabinet Ministers have claimed that Mr Johnson’s manifesto was an attempt to oust Mrs May.
This morning Home Secretary Amber Rudd accused Boris Johnson of “backseat driving” over Brexit.
Other senior Tories have said Mrs May is “too weak” to unite her cabinet and run an effective government if she fails to sack outspoken Mr Johnson.
Mr Johnson said that Britain should not pay Brussels after Brexit in 2019 and said that staying in the single market would make a “complete mockery” of the referendum.
He wrote: “We would not expect to pay for access to their markets any more than they would expect to pay for access to ours”.
This comes as Mrs May is reportedly considering to pay up to £40billion in a Brexit divorce bill in order to keep access to the single market over a two-year transition.
The article was seen by some as a bid my Mr Johnson to reignite his hopes of leading the Conservative Party.
One of Mr Johnson’s Tory MP supporters said: “He has just lobbed a hand grenade through Downing Street’s window.”
Downing Street officials did not admit to there being a rift between Mr Johnson and Mrs May.
Ruth Davidson, the Scottish Conservative leader, said: “On the day of a terror attack where Britons were maimed, just hours after the threat level is raised, our only thoughts should be on service.”
Mrs May is due to make a significant Brexit speech in Italy next week.
In an apparent backtrack, Mr Johnson has said he was “looking forward” to Mrs May’s Florence speech and he was “behind Theresa for a glorious Brexit”.