Justice Secretary David Gauke has promised to resign from his post after Prime Minister's Questions next Wednesday if Johnson wins the election for Conservative Party leader in the July 22 competition. Chancellor Phillip Hammond and International Development Secretary Rory Stewart have said it's likely that they'll join Gauke in departing the government if Johnson wins.
The three men abstained from a vote earlier Thursday in which the House of Commons shot down any future attempts to force through a no-deal Brexit without giving MPs a say - which Johnson was feared to favor. Minister for Digital and Creative Industries Margot James resigned after voting against the Conservative position and for the Labour-backed amendment. Gauke has also indicated that he would leave any future Conservative government in the event of a no-deal Brexit.
Britain is set to leave the European Union on October 31, although Parliament hasn't yet approved the deal, meaning the possibility of a "no-deal" Brexit continues to loom. Experts have warned that a no-deal Brexit, which wouldn't establish a relationship between the UK and EU after the former leaves the customs union, would cause an economic recession for the UK and be a budgetary disaster.
Johnson, a former London mayor and foreign secretary, is locked in a race with the current foreign secretary, Jeremy Hunt, to succeed Theresa May as the country's head of government next week. The Telegraph reported earlier Thursday that at this point, Johnson's lead over Hunt "looks unassailable." May announced her intended resignation last month after her administration failed to secure a Brexit deal, requiring an extension of the process, and following months of turmoil in which she was faced with multiple attempts to cast votes of no confidence against her, both by her own party and by Parliament.
The Conservative Party holds an absolute majority in Parliament, and parliamentary elections could happen no later than May 2022, although the Labour Party in opposition has repeatedly demanded that an election be called more immediately.