It beggars belief that GCHQ would send out Sean the Enforcer to say "Oy! Give us the fookin secrets or we break yer fookin kneecaps!" and the fling around 0.01% of their office equipment. Signals intelligence people simply do not do that. Actual spies rarely do it. Hell, spies in badly written television try to avoid it.
What would really happen is that a GCHQ man from Eton would call up one of his old school chums at the newspaper and they would work out some quid pro quo over tea. Quietly. Discreetly. Like professional spies.
It is barely possible that a rogue group inside GCHQ did this in a spasm of stupidity. It is just an unlikely chain of events for a rogue group to form, obtain the information, and on their own decide to make a spectacular public intervention. That sort of thing simply is not cricket.
My bet is that an outside handler goaded the GCHQ misfits squad into doing something, possibly even planting false orders. France, Russia, and China all have good reason to run GCHQ into the ground.
NSA? Not so much. Britain has long used intelligence sharing with the U.S. to punch way above their weight in international politics. The NSA would not casually throw such a valuable partner under the bus.
Whatever happened, we can at least have the satisfaction of knowing that whatever squad of fuck-knuckles organized the newspaper job are being questioned until their fingernails curl up. And then reassigned to surveil bears in Siberia.