I finally got round to fitting the Weber carb I bought off Adrian. The original Zenith was running lean no matter what I did to it.
The first issue was when I discovered that the top of the carb is 51mm whereas the Zenith is 58mm, and of course the air filter is 58mm. So I popped into Demon Tweeks in Wrexham and purchased a bit of 51mm silicon tube, cut to size and trimmed a bit it does the job nicely.
Then came the moment of seeing if it did the trick - hurrah - it runs like a dream. Bury the throttle and it just accelerates smoothly without any problem at all.
(Just remembered that the guy who had it before me, who sadly passed away, I suspect drove it with the choke out all the time. There was clip on it which prevented it being fully pushed home, and the plugs were very sooty. When I took it apart the inlet gaskets showed signs of sealant so I think someone had tried to fix an air leak in the past thinking that was the cause of the problem.)