Back to the original postings - before spending money on replacing the 'peg & socket' gears, I would take a very close look at the state of the six 'splines' on the mainshaft and those on the layshaft - plus the matching internal 'splines' on the loose gears. The ones visible on the layshaft seem to have a chamfer on one edge, rather than having a square section. I'm not that familiar with the early gearboxes, but a couple of years ago I had a problem with a Mk3 Ld which kept jumping out of gear. Replacing the loose gears didn't cure it, and in the end I had to swap out the mainshaft and layshaft to fix the problem, which was due to excessive wear on the ends of the 'splines'. TBH, a previous owner must have had a problem, as attempts had been made to 'neaten up' the ends of the splines with an angle grinder.
If you discover the mainshaft is U/S, I'd be tempted to swap the entire mainshaft, layshaft & gearset for the later 3 dog or 5 dog type. OK, so it's no longer strictly authentic, but at least the scooter would be usable!
Just as an afterthought - is everything working properly in the selector box? ( - assuming it's the early type with the spring-loaded roller.)