Meanwhile, Mr Halfon, the chairman of the education selection committee, said that while he was a “naturally loyal” conservative, there has been both a “loss of integrity” and a “policy failure”.
Several Tory MPs have begun publishing the letters they sent earlier this year, including Jo Gideon and Anthony Browne, a longtime ally of Mr Johnson who worked with him at City Hall.
Under current rules, Mr Johnson cannot face a leadership challenge until June next year when it will be 12 months since the most recent vote of no confidence.
But backbenchers have launched a plot to relieve him sooner then get this rebel-elected to the executive of the 1922 Committee and then change the rules to allow for an earlier vote and possibly a lower threshold.
At the moment, the committee chair must receive 54 letters from MPs – representing 15 percent of the parliamentary party – expressing their lack of confidence in the prime minister for a vote to be reached, and this cannot be earlier than a year after the last.
Mr Johnson won a confidence vote on June 6with 211 votes in favor of his leadership and 148 against.
One plan under discussion is to add a new rule stating that if 90 new letters – representing 25 percent of the party – are submitted, it could immediately trigger a new vote rather than having to wait for the full year has passed.
Alternatively, the threshold can remain the same, but the 12-month waiting rule can be removed.