The Electric Ballroom was in Camden Town, sort of a goth/Pcychobilly venue. I think it's still going too.
The Hammersmith Palais was a great venue, lots of bands have played there in the past. I saw a very young U2 there when they were just starting out. Killing Joke were great (my sister was a backing singer for Youths next band called Brilliant. Buts that another story). The Palais is gone now but it lasted quite awhile changing hands regularly and reinventing itself. It closed down only a few years back.
Klub Foot was also in Hammersmith, right on the Broadway. A shit hole. A hardcore Pcychobilly club. Been a few times and always wished I had gone somewhere else. Long defunct now.
The Lyceum was in the Strand, A huge old building with Doric columns etc. Again lots of big bands played there. I didn't go to this particular gig because I thought SPK were rubbish and no one had ever heard of the Smiths.
This is Matt BTW, Dean was still wearing nappies/diapers at around that time.