Lord Carey recounted his conversation with the monarch in The Real Crown: Inside the House of Windsor, a five-part ITV series.

“She would never go anyway,” he said.

He also describes how before Charles and Camilla married he arranged a secret meeting with the now Queen Consort in his son’s southeast London flat to get to know the future royal.

The series chronicles the royal family throughout the Queen’s reign and her successor the King, featuring interviews with contemporary figures.

“I remember going to see the Queen once to hand in my resignation and said ‘Your Majesty, the time has come,” Lord Carey tells the final episode of the five-part series.

“And she looked at me, more or less she said: ‘You people come and go. I can’t resign. I can’t surrender – I’ve got to keep going.’

“And I said ‘well, the Lord tells me at the age of 70 I’ve got to go’.”

Lord Carey served as Archbishop of Canterbury from 1991-2002.

He took part in the funeral of Diana, Princess of Wales in 1997 and became the first Archbishop to ordain women to the priesthood.

Lord Carey also reveals how the Queen Consort talked about the earliest days of her relationship with the King during their secret meeting in Peckham.

“She walked through the front door. We met and had coffee together and I was really struck by her,” he said.

“Very nice looking lady, very presentable, very intelligent. We had a really animated conversation and we talked about her relationship with Charles, going way back to when they were teenagers and so on.

“And after she left, I said ‘well, there’s no way I could ever treat her as other than a really nice human being who’s deeply in love with Charles’.

“And that affected me in talking to other people behind the scenes and I hoped it had a way forward. I think it did.”