I've checked the credits online and there's no composer credit for this serial. Which is odd, since it has some rather distinctive music. It has kind of a Dudley Simpson sound to it, but I'm not sure. ...Wait a minute, on second thought, I think it's tracked music from "The Moonbase." But that doesn't have a composer credit either.
The music was stock tracks, principally a piece called called Space Adventure by M Slavin (also used as you mention in The Moonbase, and also The Tenth Planet and The Web of Fear). All the various stock tracks from Tomb were put out on CD about 15 years back, though I'd doubt it's still available.
V-Sat Astra 3967 was the release number just in case it is.
Other tracks included Astronautics Theme by E Sendel, Palpitations by J Scott, Desert Storm by H Freischner and Space Time Music by Wilfred Josephs (who also did some of the music for The Prisoner).