I wish there was a Doctor Who crossover during Star Trek's original run. Patrick Troughton was the Doctor then...that would have been fantastic. But a dream is just a dream.
There's been a couple of Tom Baker-era Doctor Who
/TOS cross-overs - Jean Airey's unofficial The Doctor and The Enterprise
, and more recently some of the IDW Assimilation2
But then again, in more recent Doctor Who
continuity, Star Trek
has been referenced as a TV show in that universe - remember Rose Tyler's request to the Doctor to "give me some Spock"?
I think it's been suggested that it might be possible to fit Blake's 7 into the Trek continuity as a dystopian future, one where the Federation has turned oppressive and evil. It probably doesn't fit due to the lack of established Trek races, though.
Both shows did have Andromedans, though...
Of course, Blake's 7
is set in the 27th Century (late 2670's), so there's plenty of time for a mass die-off event to get rid of all those pesky aliens. And their planets. And all evidence of them. And anyone who ever heard of them...