PeterH:
There may be smaller options using commercial remote control products, but for an Arduino based approach you could try something like the Ciseco RFµ boards, which are Arduino clones with a small integral RF transceiver. I haven't used them myself, but they look pretty handy for this sort of thing.
Hmm that's interesting. I'd actually like to go the smallest/cheapest route, definitely not married to having it be Arduino based.
I had a google for remote controlled products but don't know which kind of thing would have multiple channels that they operate on.
Paul__B:
I would be extraordinarily surprised if they did not - because for a start, the receivers would have to be individually "paired" during manufacture.
That's a good point...
I did order one and will have a poke around once I get it.