I did LEJOG last summer, and coming through Herefordshire, my rear wheel failed completely as the brake track had worn through.
I thought I was screwed - no bike shops for miles, and it was late evening anyway. Out of desperation we were knocking on peoples doors to see if they had any wheels knocking about - the trouble was, there wasn't even many houses around. I eventually managed to buy a wheel off the caretaker at a school for £20 - basically off a dumped bike. He definitely saw me coming - it was a cheap and nasty wheel and both the axle and freewheel were initially seized solid, but eventually freed off quite nicely once forced.
We fitted the wheel and it made it from Herefordshire to Leigh in Lancashire, where I was able to stop by home to pick up a spare wheel. Suprisingly, the wheel off the caretaker worked really well, despite being a 5 speed freewheel fitted to a 7 speed bike. All the gears worked silently and it shifted well - I just had to press the shifter twice for most of the shifts.
The problem was, I needed to carry my broken wheel with me, as once I got home, I'd need the cassette off it to fit to the spare wheel.
What Carradice have you got? I just lashed the wheel to the top of mine with a belt. Looked odd, but was no bother at all. I don't see why it wouldn't be possible to lash another wheel on top of the first.
I'm not too good at posting photos, but hopefully this one will work
IMAG0493 by
Stuart Hamilton, on Flickr