As I've stated often enough, 'Doctor Who' as a TV show does exist in Earth Prime-Time - even as the Doctor exists in Earth Prime-Time as a real person. The show was probably created by some shadowy governmental organization (which I call "UNReel") to serve as plausible deniability for the Doctor's existence to the general public.
For that Toobworld-only version of the show we've met two of the actors who have played villains - Andy Millman of 'Extras' and Freddie Thornhill from 'Vicious'. Andy played a slug during the Tennant Tenure while Freddie was voted the tenth most popular villain from the show's classic period.
And since Millman played a character never seen in the Trueniverse 'Doctor Who', we can probably assume the character played by Freddie was unique to Toobworld as well.
But I do think Freddie would have done so during the Pertwee era, since we know that Jon Pertwee's televersion did play the Doctor just as the real Pertwee did - thanks to 'Supernova'.
And if we consider that Pertwee clip in 'Supernova' to be in the fictional version of the show as well, perhaps Freddie was playing the Ambassador from Alpha Centauri.....
Andy Millman (Ricky Gervais)
"The Extra Special Series Finale"
Freddie Thornhill (Sir Ian McKellan)