但是，萊斯特郡西北部的議員安德魯-布里根（Andrew Bridgen）表示，他有意加入該委員會，並參加該委員會執行委員會的選舉，他說他將 "贊成改變規則，實際上這將是另一次信任投票"。
Buckinghamshire的Wycombe議員Steve Baker也說，他希望同事們能 "考慮讓他繼續任職"，儘管他不會就改變規則發表評論。
But Andrew Bridgen, MP for North West Leicestershire, has said he is minded to throw his hat into the ring and stand for election to the committee's executive, saying he would "be in favour of rule change and effectively that would be another vote of confidence".
"The sooner the better. We will only probably have one week left before summer recess and I think we should seriously consider having another vote," he told the BBC.
Steve Baker, MP for Wycombe in Buckinghamshire, also said he hoped colleagues would "consider allowing him to serve" although he would not comment on changing the rules.
However, he added he had to "get on with the job of delivering for the people of this country".
"In the end, voters, journalists, they have no-one else to make their complaints to, I have to take that," the prime minister told reporters.
"Somebody must take responsibility and I have concluded that, in these circumstances, it would not be right for me to remain in office," Mr Dowden said.