Tory MPs have voted down proposals for a parliamentary inquiry into lobbying amid the Greensill scandal.

Labour had called for a cross-party probe led by MPs, arguing Boris Johnson’s proposed review is “wholly inadequate” as it is led by “a very good friend of the Conservative government” in Nigel Boardman.

But the prime minister ordered Tories to vote against Labour plans for the row to be examined by a new parliamentary committee, which would have been able to summon ministers and others to answer questions in public.

Labour’s motion calling for a parliamentary investigation was defeated by 357 votes to 262, a majority of 95.

Around an hour after the vote, the Commons Treasury committee said it would hold its own inquiry into Rishi Sunak and his officials’ role in responding to lobbying from David Cameron, who tried to secure Covid rescue funding for Greensill Capital, where he worked as an adviser.

It came after Keir Starmer said the Greensill scandal marks the return of “Tory sleaze”, amid questions over the former prime minister’s lobbying for the financial firm.

The Labour leader said financier Lex Greensill was brought into the government as an adviser by Cameron, before then hiring the former prime minister to act as a lobbyist contacting Cabinet ministers including chancellor Rishi Sunak and health secretary Matt Hancock.

The row has intensified this week after it emerged that the former head of civil service procurement, Bill Crothers, became an adviser to Greensill Capital while still working as a civil servant, in a move approved by the Cabinet Office.

Opening the Commons debate on a parliamentary probe, shadow Cabinet Office minister Rachel Reeves said Tory MPs would be “part of the government’s attempt to cover up Tory sleaze” by voting against Labour’s plans.

She also described Johnson’s planned review as “wholly inadequate”.

Reeves told MPs: “It’s a fact that Nigel Boardman is a very good friend of the Conservative government. 

“Some may suspect the son of a former Conservative cabinet minister might be unlikely to make waves – but let’s look at his own record.

“Boardman has been paid over £20,000 per year as a non-executive director at the Department for Business, Energy and Industrial Strategy – a department with a real interest in the British Business Bank which lent to Greensill and the British steel industry, where so many jobs are at risk.

“Boardman has already whitewashed the government’s handling of public procurement during the pandemic, and I fear he will do the same again with this inquiry.”

She added “Boardman’s law firm made £8m advising Carillion”, also telling MPs: “To cap it all off, Boardman was appointed to a prestigious role at the British Museum by David Cameron.

“What is being proposed by the government is not remotely fit for purpose. It’s not an inquiry, it’s not independent, it’s an insult to us all.”

Reeves also described Cameron’s response to 40 days of inquiries about his involvement with Greensill as “cynical” and “shabby” because it came during the national period of mourning for Prince Philip.

She said questions also need to be asked of current ministers, noting: “When it comes to lobbying, it takes two to tango. For every former minister lobbying, there is someone in power being lobbied.”

Responding, Cabinet Office minister Chloe Smith said: “We are opposing the motion today because it seeks to duplicate the work that is already in the gift of parliament and its committees and… work that is already being undertaken by the government.”

Downing Street meanwhile defended Boardman, describing him as a “distinguished legal expert”.

“He was asked to lead this review independently, he has been asked to do it thoroughly and promptly and we trust him to do that,” Johnson’s official spokesperson told reporters.

Back in the Commons, senior Tory MP William Wragg urged colleagues not to “unquestioningly defend the integrity of others if they have doubts or have been asked to do so”.

“Whatever little or imperfect integrity we have ourselves, for we are all fallible, it is the only integrity we can seek to protect,” the chair of the Commons public administration committee said.

Tory former minister Jackie Doyle-Price meanwhile said Cameron would suffer from the fallout of the scandal whatever the outcome of any review.

“The one thing that David Cameron will be concerned about more than anything else is the damage to his reputation that’s been done by this episode, and frankly that will be with him for a very long time,” she said.

Earlier, Johnson said he shared the “widespread concern about some of the stuff that we’re reading at the moment”.

“I do think it is a good idea in principle that top civil servants should be able to engage with business and should have experience of the private sector,” Johnson said.

“When I look at the accounts I’m reading to date, it’s not clear that those boundaries had been properly understood and I’ve asked for a proper independent review of the arrangements that we have to be conducted by Nigel Boardman, and he will be reporting in June.”