The former prince remains eighth in line to the throne despite being stripped of his titles in October amid pressure over his ties to Epstein.
Carney, the former governor of the Bank of England, added: “Even though he is well down the line, the point of principle stands.”
Last month Australia’s prime minister told the UK’s Sir Keir Starmer that his government would back plans to remove Mountbatten-Windsor from the line of succession.
Anthony Albanese told Sir Keir: “I am writing to confirm that my government would agree to any proposal to remove him from the line of royal succession.
“These are grave allegations and Australians take them seriously.”
New Zealand’s PM Christopher Luxon echoed Albanese’s call, telling reporters last month: “The bottom line is no one is above the law and once that investigation is closed, should the UK government decide to remove him from the line of succession, that is something we would support.”
The UK government said it was considering introducing legislation to remove the former prince from the line of succession.
Defence Minister Luke Pollard told the BBC the move – which would prevent Mountbatten-Windsor from ever becoming King – was the “right thing to do,” regardless of the outcome of the police investigation.
Speaking on BBC Radio 4’s Any Questions programme, Pollard confirmed the government had “absolutely” been working with Buckingham Palace on the plans to stop the former prince from “potentially being a heartbeat away from the throne”.