In one memo referring to a decision to publish without classification a report on interception as evidence, GCHQ said, "Our main concern is that references to agency practices (ie the scale of interception and deletion) could lead to damaging public debate which might lead to legal challenges against the current regime."
Privacy and civil liberty groups in the United States have long been suspicious of government snooping programs -- and many legal challenges were mounted based on prior evidence of such activities, such as the ongoing Jewel v. NSA case. But the Snowden leaks gave ongoing legal action more credibility and resulted in a dramatic increase in the number and variety of challenges to such activities.
The Electronic Frontier Foundation, which is litigating Jewel v. NSA, also started another legal action, First Unitarian Church of Los Angeles v. NSA in the wake of the Snowden leaks arguing the the bulk phone-records program violated First Amendment freedom-of-association rights because it gives the government a broad window into personal networks -- and the knowledge that the government is watching those could chill that association.
The American Civil Liberties Union also launched a challenge to the mass phone-call tracking program under the moniker ACLU v. Clapper, arguing that the program not only violated the First Amendment rights of free speech and association, but the Fourth Amendment right to privacy, and that the dragnet program exceeds the authority given to the NSA by the Patriot Act.
The Electronic Privacy Information Center sent a petition directly to the Supreme Court asking it to vacate a Foreign Surveillance Intelligence Court (FISC) ruling that authorized the NSA's collection of phone records on the grounds that in giving the order, the FISC exceeded its authority.
U.S. surveillance activities did have some level of judicial sign-off by the FISC, although that secret court has admitted it did not have the ability to fully investigate NSA claims and the court itself accused the NSA of misleading it repeatedly about its surveillance practices. But the legal challenges that have cropped up since show there is significant debate about the legality and constitutionality of those programs among the public.
So GCHQ was probably right that revealing the extent of its surveillance programs would lead to legal challenges. But if you're worried that the programs you are pursuing would lead to legal challenges, that might be a good sign that they aren't something you're supposed to be doing.