In addition to onewho's excellent answer, I'd like to point out how Inspector Spacetime was initially introduced into the show.
In 3x01 Biology 101, Britta gets Abed interested in a British TV show called Cougarton Abbey (because of course Britta only watches European TV), which is an obvious parody of the British series Downton Abbey (and a wink to the US series Cougar Town, which, if nothing else, you should remember from the My Diner With Abed episode).
The one thing that is important to know about real-world UK series is that they are usually quite short by American standards. The original The Office, for instance, had just 2 seasons of 6 episodes each. So Abed is devastated when he finds out that Cougarton Abbey ends after only 6 episodes, with all the main characters dying.
To cheer him up, Britta tells him of a popular British sci-fi series that has been running for decades, Inspector Spacetime (Doctor Who holds the Guinness world record for longest running sci-fi show).
This keeps Abed happy in several ways as it appeals to his new-found interest in British TV, as well as his existing passion for sci-fi, without the risk of running out of episodes to watch anytime soon.