This is a minor obsession of mine. The crew of JMC Red Dwarf are familiar with 20th Century pop-culture - but they never mention Doctor Who. Why?
In various episodes they talk about The Flintstones, Casablanca, Marilyn Monroe, Laurel & Hardy, and all sorts of TV shows. But Doctor Who is strangely absent.
There can only be one logical explanation. Lister and the gang exist the same universe as The Doctor. He has saved the Earth many times, and has deleted himself from their history.
Now, I know what you're thinking! That's pretty thin proof, right? An absence of mentioning the Doctor - even when they're time travelling - doesn't mean they co-exist. WRONG!
I present to you, two CANONICAL pieces of evidence that the TARDIS has visited Red Dwarf.
Firstly, this still from Season 3 episode "Marooned":
ZOOM! ENHANCE! PAN! ENHANCE! PRINT OFF A COPY!
According to Mike Tucker - a special effects expert who worked on the show...
There is a TARDIS model in the Blue Midget hanger from series 3 Red Dwarf– fact. (I know’ cos I put it there)
That's pretty one sided though. Just an Easter Egg for eagle-eyed fans. Nothing more to see...
WAIT A MINUTE!
In the "Eleventh Doctor Archives #1" Comic, we find the story "Spam Filtered". The TARDIS is infected with holographic spam because Rory tried to use his phone's data-connection during flight. Fool! After they land on the holospam planet, The Doctor says...
I knew a hard-light hologram once. Bit of a jobsworth.
Can you think of a better description for Rimmer than that?
There you have it - proof from both shows that they exist within the same universe. There's almost certainly a missing episode buried deep in a TOP SECRET BBC BUNKER.
If you have any other evidence, please let me know.