Boris Johnson has U-turned and ditched immediate plans to overhaul the standards system after the Tory MP Owen Paterson escaped suspension for breaching lobbying rules.

Jacob Rees-Mogg, the Commons leader, admitted the move had “created a certain amount of controversy” and had “conflated the individual case with the general concern” that there was not an appeals process for MPs who felt the punishment they faced was unfair.

Rees-Mogg said the government wanted to “achieve improvements in our system for future cases”, but that after Labour and the SNP vowed to boycott the new committee established to review the system for scrutinising MPs’ wrongdoing, he realised cross-party consensus had not been achieved.

He promised to “bring forward more detailed proposals once there have been cross-party discussions”.

While Rees-Mogg said the reforms “should not be based on a single case or applied retrospectively”, it was not immediately clear whether Owen Paterson would face the 30-day suspension from parliament or not.

“We’re in a quagmire now,” said Chris Bryant, a Labour MP and chair of the standards committee. He suggested the committee create a duplicate report suggesting the same sanction for Paterson when it meets next Tuesday, to be put to the Commons for another vote, to separate out the specific case from the general issue.

Rees-Mogg did not comment on the suggestion, but only said: “We need to have robust standards in which members have confidence.”

Tory MPs unleashed fury on Wednesday after backing an amendment by the former Commons leader Andrea Leadsom that set up a new committee chaired by Conservative backbencher John Whittingdale to review the handling of Paterson’s case and the whole standards system.

On Thursday, a government source told the Guardian: “The one proposed last night is not viable.”

Tory MPs had been put on a three-line whip and a parliamentary private secretary lost her job after abstaining in the vote, which the government won narrowly.

One backbencher who reluctantly supported the Leadsom amendment told the Guardian afterwards: “I really regret it.”

Ministers were accused by opposition politicians of setting up a “kangaroo court” and acting “like Russia”. Whittingdale admitted last night it would “prove challenging” to move forward with a committee with only Tory MPs prepared to sit on it, but he said the Commons had “passed a motion that clearly needs to be acted on”.

Johnson’s spokesman will face questions about the U-turn and Paterson’s future in a briefing with journalists on Thursday afternoon.