I don't think normal homesickness is a mental condition (I know you don't mean that but it made me smile).
The thing is, what is 'normal' homesickness? In these cases you were amongst people who were roughly the same culture 9can I use the words 'culture' and 'Birmingham' in the same sentence?) and probably operated on the same wavelength a lot.
I've lived abroad, in varying levels of isolation, and one of the tings I miss isn't food, people, TV etc... it's the chance to talk rubbish. Many of my Polish friends think I always have wonderful, intelligent conversation (or at least that's what they tell me) but what I really want to do is talk utter rubbish and stupid, pointless conversation.
Hard to do in another language or with folk who don't necessarily get it in a second language. Some jokes or comments just don't work.
Also, there is the point that you can't always find someone to off-load on (ah, the joy of the internet!) and if you try it with your local colleagues they might think something is wrong, that they've done something, when it is not necessarily anything big.