Boris Johnson is coming under growing pressure from Tory MPs to urgently replace his ethics chief to show he takes the issue seriously.
Senior Conservatives called on the Prime Minister to appoint a new advisor on the ministerial code without delay.
Lord Geidt resigned last week, after coming close to quitting over Partygate, saying he had been put in an "impossible and odious" position by the PM.
Labour wanted to give MPs the power to hold ministers to account if he is not replaced speedily, claiming that "more rule-breaking is inevitable" under Mr Johnson.
But MPs failed to back their plans for a parliamentary committee to appoint an independent ethics adviser if the role is unfilled for two months.
They voted 252 to 161 against the proposal, majority 91.
However, a string of senior Tories urged the Government to appoint a replacement for Lord Geidt as soon as possible during the debate.
Ex-attorney general Sir Jeremy Wright told the Commons: "There should not be a long gap before the appointment of a new independent adviser."
However, he said that individual should give advice directly to the PM and not to any committee of Parliament.
Former Justice secretary Sir Robert Buckland said that Lord Geidt's successor should be "appointed as soon as practicable."
Senior Tory Jackie Doyle-Price suggested ministers might not be "held to the highest possible standards" if the role was vacant for a long time.
Simon Hoare, chair of the Northern Ireland select committee, told the Commons: “This issue of ethics is proving to be a bit of an Achilles heel with the Government.”
Tory MP John Penrose, who quit as Mr Johnson's anti-corruption tsar, said he was "gravely concerned" the PM might not replace Lord Geidt at all.
Downing Street has said it accepts the role has a "vitally important" function advising on the ministerial code.
However, it has said the PM was reviewing the position and admitted he could yet abolish it.
Cabinet Office minister Michael Ellis repeatedly avoided committing to a speedy replacement.
However, eventually he claimed: "The PM intends to appoint a new ethics adviser.
"We will announce how that is to be done, and who it is and how it works, in due course."
But one Tory MP said: “Ahead of the vote of confidence, the PM promised my fellow Conservative MPs he would change, and enough of them believed him.
"If he chooses not to replace Lord Geidt, this shows them just how little his promises are worth.”
Labour deputy leader Angela Rayner told MPs that Lord Geidt had not resigned over steel tariffs as initially claimed.
"It wasn't about steel at all, it was about this Prime Minister's casual and constant disregard for the rules," she said.
"Lord Geidt couldn't stomach it any longer, and I don't blame him.
"To this Prime Minister, ethics is a county east of London - the truth is, the Prime Minister behaves as though it's one rule for him and another for the rest of us."
Ms Rayner said a "huge backlog of sleaze and misconduct" was created in the five-month period it took the PM to appoint Lord Geidt to replace his previous ethics adviser Sir Alex Allan.
She added: "This House should not tolerate a repeat performance.
"We can't endure another five months with no accountability in Downing Street, we can't endure another five minutes of this. Since Lord Geidt resigned, the Government has refused to confirm if or how his ongoing investigations will continue."
Mr Ellis also rejected Labour's plan, warning it was unsustainable for a committee chaired by opposition parties to pick an advisor for the PM.
This could lead to "disfunction, it would lead to frankly gridlock, and it would be entirely impractical and unconstitutional - it simple wouldn't work," he claimed.
He added: "In no way do I suggest that the Government doesn't regard the role with the utmost importance, we do.
"And in no way do I suggest that something of this importance will be left unaddressed, it won't.
"All I suggest is that we take a period of time to assess how to best perform this function."
