The Tories have been urged to launch a probe after it emerged a major donor was named in an international money-laundering case.
Tycoon Javad Marandi, who was awarded an OBE for business and philanthropy in 2019, "vehemently" denies wrongdoing and isn't subject to criminal sanction.
He was identified after losing a 19-month legal battle with the BBC to remain anonymous, which the broadcaster hailed as a milestone for freedom of the press.
Neither Mr Marandi nor his businesses were investigated as part of the proceedings, which arose out of the so-called Azerbaijani Laundromat international money-laundering scheme brought by the National Crime Agency (NCA).
It led to the forfeiture of £5.6 million from the London bank accounts of three members of the family of Azeri oligarch Javanshir Feyziyev.
Mr Marandi was born in Iran but grew up in London and donated over half a million pounds to the Tories between 2019 and 2020, Electoral Commission records show.
One donation of £250,000 was accepted on 12 December 2019 - the date of the general election which saw Boris Johnson win a landslide victory over Jeremy Corbyn's Labour.
He also boosted the party's coffers with £113,000 between 2014 and 2015, alongside an auction gift worth £30,000, the Commission data adds.
Alongside his wife, Narmina, the tycoon set up a charitable foundation in 2017 and supports the Royal Foundation of the Duke and Duchess of Cambridge.
Speaking in the Commons, the senior Labour MP Dame Margaret Hodge said: "There is an investigation into the Azerbaijan laundromat - $2.9billion stolen, laundered through UK companies, used to bribe politicians and line the pockets of corrupt Azerbaijan elites.
"Javad Maradi is linked with it," she added. "We should take these allegations very seriously. If true dirty money has well and truly crept into our politics."
Tory minister Chris Philp said the Government "does not and cannot comment on investigations by law enforcement operations".
"This chamber and this despatch box is not the place, cannot be the place, should not be the place, and never has been the place to comment on live investigations by law enforcement".
The Liberal Democrat deputy leader Daisy Cooper said in a statement: “If Rishi Sunak was serious about restoring integrity, he would order an independent inquiry to get to the bottom of these donations.
In a statement Mr Marandi's lawyers said: "British businessman Javid Marandi vehemently denies wrongdoing.
"At no point has Mr Marandi been investigated or questioned by the authorities. And no case has ever been brought against him or his businesses in relation to these or any other matters, anywhere in the world."
They added: "He was not the subject of this civil claim, nor a party nor a witness, meaning no evidence could have been submitted on his behalf or representations made. It is therefore unjust to be named, without having the fundamental right to rebut these false findings.
"As such, Mr Marandi is deeply disappointed at the Court's decision to lift reporting restrictions, knowing the reputational damage that is likely to follow.
"Mr Marandi and his businesses have been fully audited (with complete access to all records, institutions and third parties. Three separate reports by two highly reputed law firms, which included an investigative team headed by the former Director of the FBI and the former chief of the UK's National Crime Squad's money laundering division, and a leading financial and forensics company, have each unequivocally found there to be not a shred of evidence to support a series of conclusion by the judge.
"There the judgement, as it relates to Mr Marandi, is not only non-binding, but should be regarded as unsafe".
A Tory Party spokesman told The Mirror: “The Conservative Party only accepts donations from permissible sources, namely individuals registered on the UK’s electoral roll or UK registered companies.
"Donations are properly and transparently declared to the Electoral Commission, openly published by them, and comply fully with the law.”
