I think you also have to account that the majority of the UK population trust the Police/Security services. If not absolutely, then definitely benefit of the doubt. I feel like the US has a much much more adversarial attitude to those people. When you mention GCHQ - they're the ones who cracked Enigma etc. The NSA doesn't have that glossy veneer somehow - they are predominantly portrayed as suspicious and self serving.

I wonder if it harks back to culturally significant episodes like watergate?