Boris Johnson’s refurbishment of his Downing Street residence could be investigated by parliament’s sleaze watchdog, a move that would mean the prime minister could be personally sanctioned if found to have breached conduct rules.

The Guardian understands an extensive complaint has been submitted to the parliamentary commissioner for standards, Kathryn Stone, with powers that can lead to suspensions of MPs or even byelections if serious breaches have occurred.

The complaint, submitted by the Labour MP Margaret Hodge and seen by the Guardian, says parliament’s watchdog must probe the initial funding of the renovations, which cost tens of thousands of pounds, and investigate the possible involvement of three Tory peers.

An investigation by the standards commissioner would mean Johnson fighting a battle on multiple fronts over the payments for the redecoration of his No 11 Downing Street flat.

On Thursday, Stone committed to publicly release the name of any MP under investigation – but not until after the May elections.

The Electoral Commission launched a formal investigation into the refurbishment on Wednesday, saying there were “reasonable grounds” to suspect multiple offences may have been committed.

Johnson called the row over his Downing Street refurbishment a “farrago of nonsense”, as No 10 confirmed its own internal inquiry would not be published in full.

Speaking to reporters on Thursday, Johnson said there was not “anything to see here” but promised to cooperate fully with the investigations.

Hodge said it was essential there was now an investigation dedicated to the prime minister’s personal conduct – given the Electoral Commission’s remit was to look at the actions of the Conservative party.

“Boris Johnson has repeatedly refused to be open, honest or transparent with the donations and gifts he receives from either extremely wealthy individuals or Conservative party donors,” she said.

“We do not know who is making these donations, how much they are handing over to the prime minister or what favours they are possibly given in return for their cash.”

Hodge said she feared the three inquiries launched so far had remits that might allow the prime minister to deflect blame.

“I am deeply concerned that the prime minister will simply be able to walk away from this scandal otherwise,” she said. “The cronyism and sleaze that is rife in Downing Street cannot go unchecked, and Boris Johnson must be held to account. He cannot just wriggle out of this scandal.”

The Guardian understands another complaint has also been submitted to Stone by a separate MP.

Hodge goes on to note in her letter that “specific mention has been made in the media of three members of the House of Lords and their possible roles”.

The peers named in her letter are Lord Brownlow, the Tory donor approached to chair the Downing Street trust through which – it is alleged – Johnson hoped to fund renovations, Lord Bamford, the JCB chair whom the Daily Mail reported that Johnson wanted to approach for donations, and Lord Goldsmith, the Defra minister, whom the Mail also reported was seen as a possible donor.

“Given that they too are legislators their role is clearly of particular public interest,” Hodge wrote.

Lords Bamford and Brownlow have been approached for comment. A spokesperson for Lord Goldsmith said he had no comment on Hodge’s letter.

Senior figures in the Conservative party are said to be anxious at the potential paper trail over how donations for the prime minister’s personal life might have been solicited. Downing Street and Johnson himself have denied any wrongdoing, saying all appropriate declarations have been made and that the prime minister has met the costs himself of the renovations.

The Labour MP Margaret Hodge: ‘The cronyism and sleaze that is rife in Downing Street cannot go unchecked, and Boris Johnson must be held to account.’

In a letter to Stone, Hodge said that the prime minister would “appear to have repeatedly broken the general principles of the code of conduct, failing to be either honest, open or accountable when questioned by the media and in parliament”.

She said the prime minister’s refusal to declare who met the upfront costs of the renovation was unacceptable. No 10 has not denied reports that the Conservative party paid the Cabinet Office for the renovations, and that £58,000 was donated to the party by Brownlow for the Downing Street trust, which has not been formed, only saying that Johnson himself is now meeting the costs.

Hodge said it was legitimate to investigate the three peers as well as Johnson. She said a clear precedent had been set that donations for personal purposes should be declared after the standards commissioner ruled the Lib Dem leader, Ed Davey, should have declared a donation to buy a suit.

She said there was also the risk that public money had been wasted in terms of civil service time.

Hodge wrote that Stone should also probe the luxury holiday to Mustique taken by the prime minister last year, which she claimed had not yet been properly declared.

An investigation by Stone, if confirmed, would mean Johnson facing four separate inquiries. The cabinet secretary, Simon Case, the boss of the civil service, has been asked by Johnson to investigate how donations were declared. Johnson has also tasked Lord Geidt, his newly appointed adviser on ministerial standards, with investigating his donations.

Under the 2015 Recall of MPs Act, Stone has the power to refer the most serious cases to the committee on standards for sanctions, which can include ordering a temporary suspension of MPs from parliament. That could trigger a byelection if the suspension is longer than 10 sitting days.

In 2018, the DUP MP Ian Paisley Jr was suspended from the Commons for 30 days for failing to declare two holidays paid for by the Sri Lankan government, and lobbying on its behalf. The suspension triggered a recall petition – which would have led to a byelection if signed by 10% of constituents, though that threshold was not met.

A Commons rule change means Stone now has powers to publish the names of MPs she is investigating for breaches of the code of conduct. “I believe this step will encourage greater confidence in the parliamentary standards system,” she said.

But “in line with guidance relating to the publishing of information prior to the May 2021 elections, I will not publish the names of MPs under investigation until after the elections, in the week commencing 10 May 2021.”

Tim Durrant, associate director for the Institute for Government and author of a report out on Friday on standards in parliament, said it was legitimate to investigate Johnson as a member of parliament. “He is also an MP. If there have been donations, they should have been declared to parliament as well,” he said.

He said the rules of transparency were good but “ultimately it was down to the good behaviour of people” as there were no mechanisms to enforce them and it was a shame Lord Geidt’s remit was not wider.

“Ministers need to stop marking their own homework and allow others to enforce the rules. Unfortunately, the prime minister has not yet shown signs of wanting to make the changes we think are necessary,” he said.

Johnson has declined to commit to immediately publishing in full any findings from Lord Geidt, who is carrying out his own review of whether any donations were properly declared.

A No 10 spokesperson said Geidt would be “publishing the findings of his review, as has been the case previously” rather than the full investigation.