Ok, here's the bike:
Here are some pics of the hub:
9 equal splines so hopefully I've identified that as a Shimano Uniglide?
I think I can get the gears off if I make a whip out of a length of bar and weld on a bit of chain, stick it in gear and undo the small gear.
Basically the ratchet isn't locking up properly and if you get on the pedal too quickly the rear hub just spins.
It's an older racer, probably from around the 80's and the bloke in the bike shop told me it's an obsolete system. He said it can't be fixed and will need a new wheel, set of rear gears and probably new chain. If I try and fix it he said it'll probably be full of tiny ballbearings. Ring any bells with anyone? I'd rather fix it if I can.