Sounds like something got wedged in either your spokes or your brakes. More likely it was the spokes, as only that would stop the wheel dead. Agreed that it was probably the mudguard.

Well, I've now moved the mudguard further away from the wheel, and it's spinning freely... but there's a crackling noise as the wheel spins, as if sand grains had got into the bearings. I don't know if that could be bad enough to seize the wheel up completely. I'll take it to the Cycle Surgery on my way home tomorrow... but I'm going to be very nervous cycling it between now and then.

Maybe you need to do routine maintainance more frequently than you do atm?

I had the bike in for a full service at the Cycle Surgery just over a month ago!