Ok this is a very obscure request. I am holding a Space themed party
on New Years Eve and I'm looking for a band who I know exists as they
used to email me with details of their gigs. They play songs and dress
like the band that played in the bar/cafe that Han Solo shoots the
alien under the table in the first Star wars film. At least I think
it's the first film that was released. Anyway I'm an experienced
googler and I can't find them only an obscure reference to the Beta
Band who are not what I'm looking for. These Star wars band guys are
based in the uk so I suggest that you restrict your search to UK only.
Any questions let me know. Very obscure I told you!

I haven't found exactly what you want, but there is a new band Grand
Moff Tarkin ( http://www.grandmofftarkin.co.uk/ ).

A different band (believe it or not) of the same name, from the U.S.,
played in Star Wars costumes.

"Grand Moff Tarkin - The Band"
Now Docking ... Waypoint Station
http://www.geocities.com/dex1138/swmusic_gmt.html

Since one Grand Moff Tarkin did this, why couldn't the other?

If for some strange reason this actually works out, I would be happy
to post this idea as an answer!  Otherwise, perhaps this will be a
clue for finding another Star Wars themed band in the UK.

There is a band called Mos Eisley, after the cantina on Tatooine where
that band you spoke of played and Han Solo shot Greedo. I haven't seen
though if they do dress like that band in the movie.