The royal couple announced they would be stepping back from many of their official duties last month, January 2020, beginning a new life in Canada and trying to become largely financially independent.
Brian, who has said he will never accept a knighthood, told Britain's ES magazine that he believes their decision to move away was because of their battles with the media - which the actor puts down towards attitudes to her mixed-race heritage.
"They (some of the media) have forced Meghan and Harry to quit the country," he raged. "Let's not beat about the bush, they have driven them out, and yes, I have no doubt at all, some of it is racist. It's horrible what has happened to them."
The 73-year-old went on to explain that while he's a huge fan of current monarch, Queen Elizabeth II, the crisis over Harry and Meghan's desire to lead their own lives shows it's time to ditch the institution.
"I think the Queen is an amazing woman, and what she has done is incredible," he adds. "But when she's gone, the whole bloody shooting match should go, I really think so. We won't end this feudal hold on our culture and system until then."
Brian recently spoke about another royal encounter, claiming the Queen's sister Princess Margaret made a pass at him when he was a young actor.