Thanks for your reply.

I can't be 100% sure unless I take a core of the lawn, and I am a novice after all. However, it is thick with old grass and very spongy in places. I would say the overiding problem is the moss, it's so obviously everywhere. If the moss was gone I'm sure the true extent of the problem would be easier to determine. It would certainly look awful with the moss removed as the percentage of good grass shoots isn't great.

Maybe I should concentrate of the moss first? I would probably go for a soluble iron sulphate solution as it's cheap and fast, and a good rake when it's black. Or is it even absolutely necessary to kill it first? Then seed and feed?