Well as I worked in business I saw quite a few, the ones that come to mind are:
The Cult, before they were called the Cult at Heven
Generation X, local garage band
The Undertones at the Marquee
George Throughgood at the Electric ballroom and a pub in Camden (I still have the ticket, he is now a stadium rock star in the USA)
Squeeze at the St Dunstans school disco
Dire Straits at the local pub, the Sultan, (drummer and kit fell through the 'stage' of pushed together tables!)
The Dammed, many times at parties clubs and pubs
Dr and the Medics, many times, parties clubs and pubs
Kagagogo (well it was a free gig!)
T'Pau - turned down a job with them
Die Toten Hosen (became vast stadium band in Germany)
Boy George and Culture Club
Scritti Politti
and probably many more if I put my mind to it .....