It's not quite Star Trek, and I'm sure the BBC would have bought (and perhaps used?) its own Amigas, but on Red Dwarf series five, in the "Terrorform" episode, I'm 99% sure there's an Amiga keyboard in use.
It's shown in the scene where Lister and Rimmer are typing to each other, just after the "tarantula" has crawled up Lister's leg.
It looks like it might be an A3000 keyboard. Given that series five was filmed in 1991, that might be about right. Can anyone else confirm?
- Ali