Asking the first question of the session, Ms Leadbeater reminded the Prime Minister of the seven principles of public life and said the contest to replace him had been “unedifying”.
She said: “Summer recess gives all parliamentarians an opportunity to reflect on our ability to uphold the seven principles of public life – selflessness, openness, objectivity, honesty, integrity, accountability and leadership.
"These are fine principles but public trust in politicians is at an all-time low.
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“Will the Prime Minister be using the next few weeks to personally consider why this could be?
“And as the unedifying fight for his job continues, if those who are vying to replace him were to draw on his wise counsel – and why wouldn’t they? – what advice would he give to ensure the people we serve receive far better than they have from this Government in recent times?”
Speaking after the session, Ms Leadbeater said: “I was disappointed that Conservative MPs attempted to shout me down just as I was making the point that everyone in Parliament needs to uphold the highest standards in public life.
“All that many people see of the proceedings in the Commons is Prime Minister’s Questions.
"There were some exceptions, but many Tory MPs made my point for me today - that our politics has to change.”
Mr Johnson announced his exit from Downing Street a fortnight ago. He will continue to serve as Prime Minister until a successor is elected.
The result of the leadership contest is expected to be announced in September.