Many thanks for all your constructive replies, guys.

I did manage to get access to the valve that looks and behaves like a
bycicle one. I pushed the needle in the middle and there was a *very*
weak puff of air came out. Seems the membrane hasn't become porous after
all. The heating engineer who did the last service told me the whole tank
needed replacing and offered to do it for me on the cheap. I managed to
get some more air into it via a car tyre footpump and the range of
movement has certainly decreased. Trouble is, the maker's recommended
pressure is only 0.5 bar and I can't find an air pressure gauge that
reads such low pressure! I'll take a look on Ebay and see what's what. So
ATM it's just guesswork on my part. Still, at least there's more air in
it than there was!

Thanks again, gents.