There’s a lot of points of similarity between sitcom Red Dwarf and our own beloved Doctor Who. Both were fondly remembered British sci-fi shows before being unfortunately cancelled. Both have gotten a revival. Time will tell on how good Red Dwarf’s Series X proves to be (fingers crossed), but dammit if the idea of a crossover isn’t exciting as all hell.
Speaking to The Radio Times, cast members Craig Charles (Lister) and Danny John-Jules (Cat) both voiced their enthusiasm for such a project. Craig suggested a cameo, saying “I think it’d be great if, for one scene, we could be beaming somewhere and suddenly we’d be on the TARDIS with the Doctor. Then we could shake our heads, say ‘nah’ and just beam back out again.”
Danny on the other hand was more receptive of a full crossover, saying “I think Doug Naylor should write in one of the old Doctors. Sylvester McCoy or someone. And then we could have an episode with one of those guys in it. It would be funny.”
Admittedly, neither seem particularly likely given how the two shows are being made for and by different companies and have wildly varying styles. A non-canonical charity short is quite possible though, Doctor Who has done something similar with Little Britain.