We only know what the NSA does because a person who leaked highly confidential documents and is now a refuge for the crime of showing the world what the US govt does in secret.
Do you really think the UK govt, or any govt, doesn't use the cloak of security and classification to do questionable things?
I am just observing that the scope of GCHQ’s abilities are obviously limited compared to the NSA (unless they have the most cost-efficient IT infrastructure in the world, and we don’t do cost-efficient government IT here even now). The budget just isn’t there for them to operate the way the NSA does.
The thing you’re missing is that GCHQ spies on Americans (Foreigners from the UK perspective) using the NSA’s money, then it shares the findings from the spying with the NSA under an intelligence sharing agreement. GCHQ is mostly an outsourced wing of the NSA.
Do you really think the UK govt, or any govt, doesn't use the cloak of security and classification to do questionable things?