The actor, who currently stars in Game of Thrones prequel House of the Dragon, told the BBC's Today programme that he still pays attention to the latest goings-on in the Whoniverse, despite departing the show a decade ago.
Smith recalled reaching out to Gatwa when he was confirmed to be taking over the TARDIS in summer 2022: "I dropped him a line and said 'well done'. I always keep my eye on Doctor Who. I think [Ncuti’s] great for it, he’s totally made for it."
At the time of the announcement, Smith told press that it was a "sensational bit of casting" and that Gatwa had "something 'other' that that part really needs".
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While he evidently still follows Doctor Who with some enthusiasm, Smith admitted that he "doesn't really watch" The Crown anymore, after starring in seasons 1 and 2 as a young Prince Philip, the Duke of Edinburgh.
"I have not kept up to date with it but I’m proud to be part of it," he continued, adding that creator Peter Morgan is a "brilliant writer".
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The show became increasingly controversial over the course of a six-season run, which tackled the wedding of Prince Charles and Princess Diana, as well as the latter's tragic death in a car crash.
Smith is currently appearing on stage at the Duke of York's Theatre in London, where he plays Thomas Stockmann in An Enemy of the People, opposite Jessica Brown Findlay (The Flatshare) and Priyanga Burford (Steeltown Murders).