One task is the steering lock, which didn't have a key. NLM don't have any new steering locks, but that wasn't going to stop me finding a way

Removing the cover was easy as I've done it many times before (place a flat screwdriver under the cover and gently lever it off the sticking-out area. A locksmith showed me roughly how to try picking the lock and it turned out to be quite easy when I had a go with the relevant tools, taking perhaps 5 minutes, including soaking it with WD-40, washing it with brake cleaner, and dusting it with graphite powder alternately in between raking the pins in the lock. Levering it out took about another 10 minutes as it didn't want to come out and it was hard to find enough leverage - I succeeded by a combination of pulling with one of the lock picks, keeping the lock turned to nearly full anti-clockwise (about 80 degrees on this particular lock) so the main locking pin in the shaft was clear of obstructions, and using an old flat head screwdriver blade in combination. I also wiggled the lock a lot and sprayed yet more WD-40 and brake cleaner down the side of the lock to try and un-gunge the lock body in the shaft.
Here's a useful link (mentioned in an old post) about removing and replacing similar locks on BMW bikes http://w6rec.com/duane/bmw/lock/index.htm
My next step is to find a suitable replacement. There are various steering locks for older Vespas that look similar. My one measures roughly 39mm long with the top ridge being about 4.6mm wide. There are Vespa ones advertised at 30mm (too short) and 39mm (seems fine) and with 4mm and 6mm widths of the shoulder. The hole in the frame is about 5.6mm wide so I've ordered a wider 39mm long steering lock from a German supplier via ebay.co.uk I'd also managed to lose my cover and push-fit rivet after leaving it loose in the headstock and going for a winter test ride (oops) so I've ordered some replacement Vespa covers (5 of them) and rivet pins.
I'll post updates, including links, here. I hope this'll help some people find replacements and also the courage to try picking their own lock.