Charity regulators are investigating the activities of one of the Prince of Wales's most prominent good causes, the Prince's Foundation for the Built Environment.

The move was sparked by reports in the Guardian last month that the prince and his charity have influenced the course of a series of major property developments in the UK. The Charity Commission has announced it is seeking answers from the foundation, which is a registered charity, about whether it has intervened in planning disputes or influenced the choice of architects on projects such as the redevelopment of the £1bn Chelsea Barracks site in London.

The foundation is known to have advised on the selection of new architects for the scheme after the prince personally complained to the site's owners, the Qatari royal family, about the proposed designs by the firm of modernist architect Richard Rogers. Rogers was subsequently sacked, with the developers citing the prince's concerns, and five of the 10 firms shortlisted to design a replacement masterplan have close links to the foundation.

The foundation has vehemently denied any wrongdoing, but Republic, the campaign for a democratically elected head of state, has accused Charles of using his charities as "private lobbying firms".

The Charity Commission has now ordered the foundation to explain its trustee decision-making, the activities it undertakes to further its charitable purposes for the public benefit, and its relationship with Prince Charles.

Further questions were raised after the Guardian revealed that the prince intervened to try to change the architects for a £500m development next to St Paul's cathedral, and that his aides regularly scrutinise plans by major architects including Sir Terry Farrell, Sir Richard MacCormac, John McAslan and Alan Baxter, who work on some of Britain's largest building projects. The foundation describes itself as an educational charity.

"The Charity Commission's involvement indicates there are serious questions to be answered about the relationship with Prince Charles and the charities he has set up and whether they are pursuing a public good, or working for Charles's benefit," said Graham Smith, a spokesman for Republic, which lodged the formal complaint about the foundation.

It included the claim that Charles, who is the charity's president, "is deliberately using the charity to usurp democratic planning processes and ensure his preferred architects are hired by developers".

In a letter to Smith this week, the Charity Commission thanked him for bringing the matter to its attention and said that while in law the prince can appoint trustees of a charity, "trustees appointed by the prince have the same duties and responsibilities as other trustees and they need to only act to further the charity's purposes for the benefit of the public".

The prince is understood to be closely involved in the charity's management.

Hank Dittmar, the chief executive of the foundation, strongly denied that the charity was acting in breach of charity law.

"The Republic complaint to the Charity Commission is unfounded and baseless," he said.