I got an upper second eleven years ago, as did the majority of my year group. These days I just say, "I have a degree," and no-one asks or is really bothered about what class of honours I got. When I apply for jobs, although I always put the classification on my CV, I never get asked about it. People just ask more general questions about what I studied and how I used the experience of uni.
I guess, as Buenchico says, if you're going into certain professions or if you want to go on to further study, it would matter, but you've already said you're not worried about that.
I know my Bro-in-Law got a first at Oxford (brainy s*d!) in the late 60s, and that did help when he left teaching and became a civil servant. He's now pretty high up in the service, something which is probably due in no small part to the old school tie network, but I'm not sure that honours classification ever came into it.