On Sunday, protesters on the Garvaghy Road were joined by members of Sinn Féin, including O’Neill, and the Social Democratic Labour Party.

The Democratic Unionist Party subsequently accused O’Neill of acting unlawfully as notice of the protest had not been lodged.

Sir Chris said “nobody should be attending an unlawful protest”, but he added it was not his job “to decide whether somebody has or hasn’t broken the law”.

Assistant Chief Constable Ryan Henderson has said a “dedicated enquiry team” had been established, which was currently reviewing evidence gathered and “anyone who has broken the law will be investigated”.

The Portadown District of the Orange Order also lodged a complaint with the chief constable in relation to O’Neill and McDonald’s attendance.

In a statement on Tuesday, the County Grand Orange Lodge of Belfast said its position was clear.

“There is a lawful Parades Commission determination in place. This has been upheld by the courts,” it said.

“It is now for the PSNI to uphold the rule of law and facilitate the completion of the return home.”

The Deputy First Minister, the DUP’s Emma Little-Pengelly, criticised O’Neill for travelling to Dublin instead of attending the Northern Ireland Assembly on Tuesday afternoon and rejected suggestions her party was raising tensions.

Little-Pengelly argued it was O’Neill who was “on the Garvaghy Road at the weekend chanting, encouraging people to break the law”.

“She needs to come to this house and answer questions and subject herself to that scrutiny,” she added.