Housing Secretary Robert Jenrick will not appear in Parliament to answer a question from Labour relating to his approval of a £1bn property scheme.
Planning minister Chris Pincher, junior to Mr Jenrick, will face MPs instead.
Labour says Mr Jenrick is “hiding from scrutiny” – but sources close to Mr Jenrick say he will face MPs on Monday at his regular question time.
The row centres on a £12,000 donation to the Tories by property developer Richard Desmond.
The Conservatives said policies were “in no way influenced by donations”.
Mr Jenrick granted planning permission on 14 January for Mr Desmond’s company Northern & Shell to build on the Westferry Printworks site on east London’s Isle of Dogs.
It has emerged that Mr Desmond made a personal donation to the Conservatives on 28 January.
The property development was approved the day before the introduction of a new council community levy which would have meant the company paying an additional £40m.
In approving the project, Mr Jenrick overruled the Tower Hamlets planning inspector who said it needed to deliver more affordable housing in London’s poorest borough.
The council has since challenged the decision, forcing the secretary of state to back down and to admit what he did was “unlawful by reason of apparent bias”.
Local councillors asked the High Court last month to order the government to disclose emails and memos around the deal.
Rather than doing this, Mr Jenrick’s lawyers conceded the timing of his decision “would lead the fair-minded and informed observer to conclude that there was a real possibility” that he had been biased.
The £12,000 figure was included in Tuesday’s Electoral Commission audit of party donations for the first three months of the year and first reported by the Daily Mail.
Mr Jenrick has come under growing political pressure in recent weeks after it emerged he sat at the same table as Mr Desmond, the former owner of the Daily Express, at a Conservative Party fundraiser last November.
A spokesman for Mr Jenrick told the Daily Mail that “the developers did raise their application, but Mr Jenrick informed them that it would not be appropriate for them to discuss the matter with him, or for him to pass comment on it”.
But Labour said Mr Jenrick must now make clear whether he told officials at his department about the meeting and disclose whether he or members of his team had any other contacts with the developer.
Unless the housing secretary published all documents about the application and any correspondence with Mr Desmond in the run-up to the decision, the opposition said, “the public will be entitled to think it’s one rule for the Conservatives and their wealthy friends, and another rule for everyone else”.
“Communities must have confidence that the planning process is fair and transparent, but the unanswered questions around Robert Jenrick’s unlawful decision have weakened that trust,” said Labour’s shadow communities secretary Steve Reed.
“It’s time for Mr Jenrick to come clean and answer these crucial questions about why he over-ruled his own inspector to grant planning permission for a billionaire Conservative Party donor to build a luxury development.”
Andrew Wood, who resigned as leader of the Conservative group on Tower Hamlets Council because of his concerns over the property deal, has called for the Cabinet Office to launch an investigation.
He told the BBC details of Mr Desmond’s donation raised “more questions about what was going on”, adding that although £12,000 was “not a lot of money,” it did not look good.
“The optics are terrible,” he added.
A Conservative Party spokesperson said Mr Desmond’s donation had been properly declared to the Electoral Commission and fully complied with the law.
“Government policy is in no way influenced by party donations – they are entirely separate,” the spokesperson said.
Mr Jenrick has insisted there was no actual bias towards Mr Desmond but said it was right for the decision to be revisited to “ensure there was complete fairness”.
A spokesman for the Department of Housing, Communities and Local Government said that, while “we reject the suggestion there was any actual bias in the decision, we have agreed that the application will be re-determined.”
Mr Desmond has, in the past, donated money to both Labour and UKIP.
Northern & Shell, of which he is the majority shareholder, sold its publishing interests in 2018 and now focuses largely on property development as well as digital ventures and the Health Lottery.
Former Labour Transport Secretary Lord Adonis has written to the Cabinet Secretary about the matter. Writing on Twitter, Lord Adonis said he would raise Mr Jenrick’s “failure to answer parliamentary questions about his conduct” in the House of Lords.