Wow, thanks for all the responses so far!! I'm relieved that no-one is calling me some bitter child hating harpy!
I have already spoken to my very close friends who have children (none are still bfing), and they didn't mind at all. It is easier for them as the wedding is pretty much local to where they live. In my wider family, I would obviously prefer that they came without the kids - especially since I know for a fact that they have family (not on my side) very near by who could take the kids, and who they are very close to - but at the end of the day, if they don't want to for whatever reason, then that is completely their choice, and I wouldn't resent them for it.
For my wider family there would be limited travel involved, but no more than 45 minutes.
We decided to go for no children under a certain age (10 or 11), as that ruled out the vast majority - all the other "non adults" would be 10,11,14,16, etc.
Thing is, I do have a relative with four children, only one of which is over the age limit. I was going to invite the older child with them but not the younger ones (who are all under 5). Maybe that would be more awkward?
It's a little more difficult on my partner's side as they are travelling much further. Then again, the people it would actually affect are family members that he hasn't seen in years anyway. So he would be happy to see them, but no big deal if they don't fancy travelling, if you see what I mean. The rest of the children in his family are over the "age limit".
I wanted to avoid the "only close family can bring their kids" as I don't have any immediate family with children anyway, and I didn't want anyone to resent the fact that they were told they couldn't bring their children, but Sally-Jo could bring hers, iyswim.
I can understand when people say that weddings are supposed to bring all the generations together, but I also think that's quite a traditional way of looking at weddings (not that there's anything wrong with that). Maybe I would feel differently if I saw these children all the time, but I've only ever met them a handful of times anyway.
I've been to weddings with and without children - they definitely have a very different atmosphere, but I've definitely noticed that people seem more...relaxed (?) if they aren't in parent mode.