Google does have a
detailed legal process, which makes it pretty clear that Google sees itself operating as a U.S. institution, and external requests need to go through MLATs between other countries and ours. I'm guessing that the UK wants something far more direct than this.
Google, the parent company, may see themselves as a US institution, but they do have subsidiaries in many other countries (including one in the UK). So if their Chinese subsidiary was beholden to Chinese censorship laws, I can't see why their UK subsidiary wouldn't be beholden to the UK snooping laws.