The air filter consists of a oil reservoir with a plastic mesh/sponge filter leading up into the system. I've ditched the old oil as it was clearly contaminated and was looking a bit emulsified. I need to refill it with something, but I know it wasn't the cause of the engine death.
I removed the carb and gave it a few days of drying inside the house, and I flushed the petrol tank the other day and left it to dry on the underfloor heating. I put the whole lot back together again yesterday and gave it a little FRESH petrol and a single squirt of Easi-start. Result: started second pull. Very pleased with the result, but also with myself for managing this after being such a numpty in the first place.
The engine is running a little unevenly, though not rough, and when I put the blades into gear it kills the engine once I start moving. I'm working on the assumption - after much thought last night - that it is because I'm not giving it enough revs once the blades are doing the work. I'll give it another try this morning.
It'd help if I knew what all four handlebar lever were for: one if the dead-man's clutch, one allows the handlebars to be pivoted to the side while it's in motion - for keeping out of the way when ploughing, presumably, and I think one of them is a brake.