There is no suggestion of any wrongdoing by either party, but the details have raised further questions about the judgment of the future king.
The Sunday Times reported that on one occasion the cash from "HBJ", as Sheikh Hamad is known, was stuffed into Fortnum and Mason bags.
Sources told The Telegraph that some of the details of the handovers are disputed and the prince maintains that he has not broken any rules.
The meetings in which the money was handed over were private and therefore do not appear in the Court Circular. In a 2015 meeting at Clarence House, the 73-year-old prince is said to have accepted a holdall containing €1 million.
It is alleged that the cash was handed to Royal aides who counted out the now discontinued €500 notes, which were named the "bin Laden" because of links to the funding of terrorism.
One former adviser who handled some of the cash said that "everyone felt very uncomfortable about the situation".
Private Coutts bank, which has served the Royal Family for decades, then collected the cash and it was paid into the accounts of the Prince of Wales's Charitable Fund (PWCF). There is no suggestion that the payments were illegal.
The PWCF is a grant making charity that has bankrolled a number of the prince's personal projects, including Dumfries House in Scotland.
A Charity Commission spokesman said last night: "We are aware of reports about donations received by the Prince of Wales' Charitable Foundation. We will review the information to determine whether there is any role for the Commission in this matter".
Guidance from the regulator
Charities can accept donations in cash, and the regulator issues guidance for trustees on how they should deal with any donations in compliance with the law.
Sheikh Hamad, 62, one of the world's richest men, oversaw Qatari investment in some of London's prime real estate in his time in office, including Harrods and the Shard.
But his time in office was also marred by allegations against the emirate of financing the Syrian branch of al-Qaeda and of bribery and corruption surrounding the 2022 World Cup bid.
It is the second time this year that donations to the Prince's charities have been called into question, with the Metropolitan Police currently investigating allegations of cash-for-honours.
Michael Fawcett, a close confidant of the Prince, is alleged to have attempted to secure a CBE for the Saudi billionaire Mahfouz Marei Mubarak bin Mahfouz, who had given more than £1.5m to the Prince's Foundation charity.
The PWCF did not respond to requests for comment on Sunday.
"No failure of governance"
Sir Ian Cheshire, the director, told the Sunday Times that they "have checked into this event in the past, and confirm that the previous trustees of PWCF discussed the governance and donor relationship, confirming that the donor was a legitimate and verified counterparty and our auditors signed off on the donation after a specific enquiry during the audit. There was no failure of governance".
Charity Commission guidance states that trustees should consider whether donations are made under an "unusual payment mechanism" or are from countries with weak financial regulation.
It states that trustees should report donations of £25,000 if it is an "unusually large one-off donation or a series of smaller donations from a source you cannot identify or check".
The policy on Royal gifts states that members of the Royal Family can accept cheques for charitable causes but does not mention cash.
Speaking from the G7 summit in Germany, Boris Johnson's official spokesman declined to comment on the allegations as part of a long-standing convention that the Prime Minister does not address royal issues.
The spokesman also declined to comment on whether Johnson himself would accept charitable donations from a cash-filled briefcase.
Brandon Lewis, the Northern Ireland Secretary, said that it was not a matter for the Government, but he was confident the donations would have gone through "proper due process".
A Coutts spokesman said that any cash payments "receive thorough review and oversight".