The British parliament is to investigate Prince Charles's controversial role in helping to shape government legislation in a move likely to increase pressure on Whitehall to reduce the secrecy around alleged royal lobbying.

MPs will examine the heir to the throne's little-known royal veto over any new laws that affect his private interests next month. The move follows a Guardian investigation in 2011 into the secretive constitutional loophole that revealed how ministers have been forced to seek permission from the prince to pass at least a dozen government bills.

The House of Commons political and constitutional reform committee, chaired by the Labour MP Graham Allen, will ask whether there is a risk that the requirement of royal consent, which is also granted by the Queen depending on the nature of the law being passed, "could be seen as politicising the monarchy".

It has emerged that Charles has held 36 meetings with ministers since the government took power in May 2010. He has met the prime minister, David Cameron, seven times, four different ministers in the Department for Communities and Local Government and held six meetings with ministers in the Department of Energy and Climate Change, which oversee areas in which the prince campaigns on planning and the environment respectively. Neither Whitehall nor Clarence House will elaborate on what was discussed in the private meetings.

The royal veto is seen by some constitutional experts as a nuclear deterrent – a red button that is unlikely to be pressed but that may focus ministers' minds when Charles and other members of the royal family discuss policy matters with them.

Later this year, the court of appeal will hear the latest stage of an eight-year battle by the Guardian to get the government to reveal a set of 27 letters written by the prince to ministers in seven departments over a nine-month period.

The questions being asked by the committee, whose members include the historian Tristram Hunt, include: "Is there a continuing justification for the Queen's or prince's consent to be part of the legislative process?"

Allan said seeking Charles's consent to laws that affect his interests was "a relic" but stressed his focus was on how the executive may manipulate the royal prerogative to push through decisions without the proper scrutiny of MPs.

Both Clarence House and Buckingham Palace said it was "a long-established convention" that the prince, as Duke of Cornwall, is asked by parliament to provide consent to those bills that parliament has decided would affect Duchy of Cornwall interests. They said the same process is followed with regards to the Queen providing consent to bills that would affect Crown interests.

"In modern times, neither the Queen nor the Prince of Wales has refused to consent to any bill affecting Crown, Duchy of Lancaster or Duchy of Cornwall interests, unless advised to do so by ministers," the palace said. "In matters of legislation, the Queen always acts on the advice of the government. Every instance of the Queen and the prince's consent having been sought and given to legislation is a matter of public record."

Anti-monarchy campaigners welcomed the MPs' inquiry.

"If Charles believes he has a right to secretly lobby ministers and exercise a veto over new laws then he should be called to the Commons to give evidence himself," said Graham Smith, director of Republic. "It's no good Charles sending his PR men to give evidence, he needs to turn up and explain himself in public. He seems keen to meet MPs in private, now is the time to hear what he has to say out in the open."

No members of the royal family or their staff are expected to be called to the three hearings scheduled for September, Allan said.

Since 2005, ministers have sought the Prince of Wales's consent to draft bills on everything from road safety to gambling and the London Olympics. Unlike royal assent to bills, which is exercised by the Queen as a matter of constitutional law, the prince's power applies when a new bill might affect his own interests, in particular the Duchy of Cornwall, a private £847m property empire that last year provided him with an £19m income.

The government tried to block the release of further information about the extent of the power enjoyed by the Queen and Prince Charles, but earlier this year Whitehall papers prepared by Cabinet Office lawyers were finally published, showing at least 39 bills have been subject to the most senior royals' power of consent.

They also revealed the power has been used to torpedo proposed legislation relating to decisions about the country going to war. In the pamphlet, the parliamentary counsel warned civil servants that if consent is not forthcoming there is a risk "a major plank of the bill must be removed".

In one instance, the Queen vetoed the military actions against Iraq bill in 1999, a private member's bill that sought to transfer the power to authorise military strikes against Iraq from the monarch to parliament.