Update on previous post. My scepticism was well founded after all and the confident diagnosis froM Celtic mowers was incorrect. After replacing the fuel, the mower ran well for a while, but the chugging and black smoke returned.
I decided to go with other posts and replace the diaphragm. The good news is that you only need to buy the diaphragm replacement kit and not the full S2 kit. Get part number 795083 from Briggsbits.co.uk for £5.87 including shipping. The other good news is that it's easy to change. See an excellent video on YouTube - http://www.youtube.com/watch?v=C5nzigcNTwo&sns=em
There are two gaskets - a normal sealing gasket and a thin rubber one which are both sandwiched between the carburettor and the fuel tank. Just two bolts release the carburettor and and fuel tank as a unit, making the rest easy. The only fiddley bit is releasing the throttle linkage (but not difficult). Also watch that the rubber sealing ring and it's retaining clip may come off onto the intake manifold (as it did with me). Easy to pop it back into the carburettor before rebuilding.Clean as you progress with lots of carb cleaner.
On inspecting the old rubber diaphragm, the problem seems to be that a small round area with a spring behind it functions as a crude pump and this part had become stretched.
All back together and working well. Spark plug still clean after a prolonged run.
I think I've finally cracked it!
Ospreylian, August 2012