Boris Johnson is facing warnings from his own MPs that he urgently needs to rebuild public trust after admitting he “crashed the car into a ditch” in the row over standards at Westminster.

Deputy Prime Minister Dominic Raab insisted ministers are committed to “fixing the problem” amid continuing frustration and anger among Tory MPs at the damage that has been inflicted over the past weeks.

At a private meeting of the Conservative backbench 1922 Committee on Wednesday, Mr Johnson took responsibility for the Government’s botched attempt to get Owen Paterson off the hook after he was found to have broken the rules on paid lobbying.

“On a clear day I crashed the car into a ditch. I will get the car out of the ditch,” he reportedly told the gathering.

Mr Raab acknowledged the Government has a job of work to do to restore morale within the Conservative ranks after seeing the party engulfed by allegations of Tory “sleaze”.

Asked on Sky News about discontent within the party, he said there is always “one or other disgruntled individual” who is prepared to complain anonymously in the media.

Pressed on whether that means there is no general unrest, Mr Raab added: “Not sure I’d put it in that idyllic way. There’s always debate amongst MPs, but the most important thing is we’re fixing the problem.”

On Wednesday, the Commons backed Mr Johnson’s proposals to ban MPs from taking paid political consultancies and to limit the time they can spend doing second jobs.

However just 297 MPs – fewer than half the total – voted for the motion, with opposition parties abstaining.

Four Tory MPs even voted for a rival Labour motion which would have imposed a clear parliamentary timetable for implementing reform.

Shadow chancellor Rachel Reeves said there is a lack of urgency from the Government when it comes to dealing with the issue.

She told BBC Radio 4’s Today programme on Thursday morning: “The problem with the amendment from the Government which was passed yesterday is that there is no timetable.

“It wasn’t a binding vote and, as a result, I just fear it is going to be kicked further into the long grass rather than the fundamental reform that people want and need to see now to restore confidence in our parliamentary democracy.

“I think that public service and being an MP is something that I am proud of and I think most MPs are, but at the moment you don’t feel that proud. People look at MPs and just think it is just mired in sleaze.

“I think we need to sort this out quickly to restore the reputation of Parliament.

“It seems that Government just don’t have that sense of urgency about restoring people’s faith and trust in our parliamentary democracy.”