I'd assume they'd go along with government policy, like they have done in e.g. China. And the government proposed taking down twitter and BBM during the London riots a few years ago.
I'm afraid you might be a tad ambitious regarding the weight the UK market carries with global corporate interests, as compared to the Chinese
I'm not so sure. It only takes one browser vendor with a significant interest in the UK (Google would be a good candidate, given that advertisers are very sensitive to legislation) to make the whole exercise useless.