Sadly, somebody at some point had driven off without lifting the jockey wheel, so the plastic wheel was "proper wrecked" as they say, and wouldn't roll anywhere.
Also, and this is my fault, as the jockey wheel was off the chassis, I didn't check that the little lever that clamps the thing in place was tightened up properly and it shook loose somewhere between Stratford and our house. Learning point there.
Through luck and good scavenging, I already had a nice little wheel with a pneumatic tyre that I found in a skip about a decade ago. It had stayed inflated for a couple of days, so I don't think I need the puncture repair kit just yet.
So, I've joined those together with a random selection of washers and it all turns quite nicely. The wheel has proper bearings and all. I've bent an M12 coach bolt to replace the lever - I've just got to add a "stop" for it to operate the clamp properly (hole, washer, split pin, I think) and we have a nicely rolling chassis.