In her reply to Mr Johnson’s letter of resignation, Mrs May said she was “sorry - and a little surprised” that he had chosen to leave following their “productive discussions” at Chequers.
However, she said that if he was unable to support the Government’s agreed position “it is right that you step down”.
“As I outlined at Chequers, the agreement we reached requires the full collective support of Her Majesty’s Government,” she said.
“During the EU referendum campaign, collective responsibility on EU policy was temporarily suspended. As we developed our policy on Brexit, I have allowed Cabinet colleagues considerable latitude to express their views.
“But the agreement we reached on Friday marks the point where that is no longer the case, and if you are not able to provide the support we need to secure this deal in the interests of the United Kingdom, it is right that you should step down.”