I don't not drink, but I don't drink that much either (i.e. I usually have only a couple of drinks a month). I'm also usually driving to and from social events, so I often end up not being able to drink anyway, even if I wanted to.
I've never found it an issue before - I just say I'm having a Coke or whatever, and no one says a thing.
Don't be put off by work invites involving the word 'Drinks' though... that's usually just standard wording for 'a social event after work, usually in a pub'. Also, just because it's in a pub, it doesn't mean you have to drink alcohol - many pubs are kid-friendly and will be used to catering for non-drinkers.
I did a work placement at my company HQ a couple of years ago, and the first week, my supervisor sent round an email inviting everyone to the pub after work... only a few of us actually had an alcoholic drink because most of us were driving.