Here you see and hear a happy, working mower. I fixed it. There were several problems, some of them were of my own making.
The first problem, that was the root cause of all the hassle, was that I incorrecty fitted an air filter. This caused grass cuttings and other rubbish to get into the carburetor and clog it, but also, a part of the rubber seal broke off from the filter and wedged itself in the carb's main venturi.
The second problem was that the starter motor was shot, or rather its brushes were. This meant that the mower was hard to start at the best of times, and it was a while before I twigged that the problem was not down to lack of battery power. I bought and fitted a new starter motor.
The third problem was that after removing and cleaning the carb, I tried to ensure that it was full of petrol by connecting a funnel to the fuel pipe, and pouring petrol down it. Mistake. The petrol then flowed out of the carb and into the moulded plastic air duct that sits between the air filter and the carb.. I admit I forced it a bit. The engine ran rich. Not surprising really; the incoming air was probably bubbling through petrol. I was lucky the whole lot didn't catch fire. Or explode.
I learnt something else too. I got a quote for a new carb from an official (perhaps the official) importer of the parts into France. Just over €290. For a carb. Here is a link to an eBay seller in the USA selling what is either identical or equivalent for less than $35 US. Just... wow.
It took me a couple of days' work to fix the mower, stretched over about 4 weeks. Fortunately the grass wasn't growing much since it was the height of Summer, so not a problem. I learned a bit, and saved a lot of money.