Doctor Who in the Star Trek universe
My simple theory is that the Peter Cushing films are part of the Trek universe - but does that work? I mean, I'm not overly knowledgable on Trek yet. The second one was set in 2150, when the Daleks invaded Earth.
I just think these beasts suit Trek, especially TOS:
"Now you are asking me to sabotage that achievement, to send them back into the dark ages of superstition and ignorance and fear? No!"
~ Captain Jean-Luc Picard