Season 4 is expected to cover the late 1970s through 1990 and feature the courtship between Charles and Diana, known before her marriage as Lady Diana Spencer.
The Crown follows the life and reign of Queen Elizabeth II, played by Claire Foy in Seasons 1 and 2 and Olivia Colman in Seasons 3 and 4. Menzies said Season 4 will have a new focus on Elizabeth and Philip's children, including Charles.
"In a way, the kids start to come into the foreground," the actor said. "Charles comes into the foreground, Diana is a big part of Season 4. Thatcher obviously, which is quite interesting given she is the most divisive political figure that the show has had to represent thus far."
Menzies said Anderson was "looking remarkable" and "incredibly" like Thatcher during filming.
"It will be interesting to see how that is received," he said of the Thatcher storylines. "All the other political figures are far enough in the past that there is less heat around them."
Menzies said his scenes for Season 4 and the "vast majority" of the season were shot before production shut down due to the coronavirus (COVID-19) pandemic. Netflix has yet to announce a release date.
Menzies made his debut as Philip in Season 3, replacing Matt Smith, who portrayed the prince in Seasons 1 and 2. He said in an interview with The Hollywood Reporter last week that taking over the role from Smith was a "very curious, unusual" experience.
"It was a hugely successful show, so you kind of know what you're getting into. But I had to forget all that and reset," the actor said.
"It's a bold decision to recast everyone and then carry on with a whole new set of actors. So I think we took refuge in going, 'We're just going to make this our show, the best we can,'" he added.