Ok. For a start, if the company holding the data is the Uk subsidiary, they should not be forced to provide data under US law. As someone who works for zn international firm, I can assure you it can get annoying when even though you are head office, you have to comply with local regs.
Putting that aside, why on earth would the US want that data and what will they do with it? If we get to the stage where the CIA is somehow rounding up peole in middle England, then quite frankly, we have gone so far beyond issues of privacy that the discussion is irrelevant.
I honestly do not understand this idea that big companies are out to do something nefarious. For a start, do you even know how hard it would be to create an environment where you could do that? Frankly, it's far more likely in a small firm. "businesses" don't have giant, world manipulation plans.