Well, according to the article, there was only the one family that caused the uproar.
Isn't that typical of the way we respond to problems? Somebody's panties get in a wad and we fall all over ourselves catering to that single complainant.
It looks to me like the restaurant owners have done a risk analysis and have concluded that the risk of offending a single customer does not outweigh the risk of allowing kids to run around the restaurant like a bunch of Chucky Cheesers.
Furthermore, I might be off target here, but I'd say that generally, the decorum and general demeanor of those eating out in the UK might be a little more subdued than we find here.
Case in point - yesterday I went to a Chili's restaurant to eat a meal. Sat at the bar, because I was by myself. The restaurant was so damned loud I couldn't even hear the person sitting next to me as we engaged in a bit of chit-chat. And it had nothing to do with unruly kids -- it had everything to do with there being a lot of people and a lot of activity.