So the plan was to book it in for a roadworthy, fix anything required for that and then enjoy driving it for a bit and improve bits and pieces once it was on the road...
I thought I'd give it a service first for peace of mind, but the job grew a little. I gave the engine bay a good degrease and pressure wash, dropped the oil, changed the oil and petrol filter, replaced some split fuel line and checked the plugs (which, surprisingly, looked fairly new). Then I flushed the radiator and after a close inspection, decided to remove it to have it professionally cleaned, painted and pressure tested.
Unfortunately, once it was out and sitting on the bench, it was obvious that it had seen better days, which was confirmed by a local radiator shop. The guy suggested I either get it re-cored, or for basically the same cost, purchase a replacement Adrad unit. I opted for the latter, so now I have a nice, clean, shiny new radiator.
I could hardly fit that up with old hoses and clamps, so I jumped online and bought a new set, and that's when the quick service turned into a bit of a small project!