I think the universal description of WW2 as 'the war' is because of the nature of it as a war that directly effected everyone and dominated, wholeheartedly, the entirety of life. It's the first time Britain faced 'Total War', and thus it was rather like everyone was involved. Every other war we can detach ourselves from, we weren't being bombed, we weren't being called up, home life was more or less the same.
I suspect that if we had another war that was on our soil, literally, in one way or another, we'd come to refer that as 'the war' in time, especially if it's impact was great enough.