Ivor,
I was thinking new chain would help, but I am thinking of a different bike.
Before I went after the cases with anything, I would take this down a ways and really look at what you have. Something seems off.
This reminds me of a millwright I know who always says "its really easy to take it off, its not so easy to put it back on" (meaning removing metal with a file, grinder, hacksaw, torch, lathe, mill, large hammer
)
Lee