Gears randomly shifting?

Thanks for the responses.

It seems that adjusting the L&H screws may not be the solution. The chain is not slipping off the freewheel - ie no over or undershifting is occuring. The gears are shifting correct.

The slipping happens in any gear so don't think it is worn teeth on the cassette.
Chain tension or arm tension sounds closer to the problem. When I turn the pedals the chain just doesn't have enough tension to take hold of the rear cassette.

How do I resolve this? Would I still need to adjust or reindex cables?

have a look on youtube by searching 'adjusting rear derailleur cable tension' and there are a few videos that will show you how to do it. also, as was mentioned, your cable might have rusted inside its housing, so it'd be worth checking that. you can adjust the tension all you want, but if the cable is sticking, you'll always have problems.

good luck.