So, a bit of progress. Put everything back together, fitted a new air filter, filled the tank with fresh fuel mix and tried starting. 
Sounded like it was hitting a couple of times but wouldn't keep running. Pulled off the decompressor, checked it closed when vacuum was applied (it did) so reinstalled with a new crush washer stolen off a fairly new spark plug.
Next pulled the muffler off, exhaust port looks pretty clean and piston looks good, but tapped the muffler on the ground and quite a lot of carbon came out. Thought I'd flush it with water to make sure it was clear but the water doesn't seem to flow out again, so assume it's badly blocked.
With the muffler off, engine will run with throttle wide open for 4 or 5 seconds before cutting out.
Pulled the bowl off the carby, destroying the gasket in the process, and had a look inside, collected some fairly horrible looking fuel in the container I was using to catch the fuel but it may well be dirt from the outside of the bowl because it was pretty grubby. 
Anyway, have ordered a carby kit and will replace everything I can from the kit. Any reason I can't put the carby in a tub of carb dip to make sure it's clean? Not sure what plastic parts are inside that I can't see.