Mr Johnson survived a vote of confidence by 211 to 148 on Monday night (June 6).
So far, only Sally-Ann Hart, Hastings and Rye MP, has admitted to backing the PM.
As Nus Ghani, Wealden MP, is vice-chair of the 1922 Committee, she helped oversee the vote as a ‘neutral adjudicator’.
She said: “I must remain as such to oversee any future votes that may or may not take place. It would therefore not be appropriate for me to comment on whether I have submitted a letter of no confidence or which way I voted.
“I recognise that Conservative MPs have voted by 211 to 148 that they have confidence in Boris Johnson as leader of the Conservative Party.”