Sir Alan Duncan has quit as a Foreign Office minister in protest against a possible Boris Johnson victory in the Conservative leadership race.
Chancellor Philip Hammond and Justice Secretary David Gauke have already said they intend to resign if he wins.
BBC assistant political editor Norman Smith said they could not stomach the prospect of a no-deal Breixt which they think Mr Johnson could oversee.
Voting for the leader closes later with the winner to be revealed on Tuesday.
The successor to Theresa May – either Mr Johnson or his rival Jeremy Hunt – will enter Downing Street on Wednesday.
Tory leadership race: Alan Duncan resigns as minister}