REJOICE!
Andy Gates, for t'was he, has fixed it.
The fault? With me riding and Andy running behind, it was obvious that the tensioner was catching the chain in some way (we still haven't figured out how) causing the chain to skip. Andy introduced me to the concept of a 'magic gear' eg one that would work without a tensioner. The only one that was achievable with the bits that I've got was a 53x18. I'll be gurning up hills like a chimp treading grapes but at least I'll be riding.
NOT the freewheel
NOT the chain
NOT the chainwheel
NOT the sprockets
Just some weird random and totally inexplicable juju. Thanks for all the advice and suggestions though, they were appreciated.
In the meantime I'm going to develop thighs like Chris Hoy. Then I'm going to buy a new chain tensioner and go back to my nice comfy 46x16...