As you can appreciate it can be hard to get reliable sources when the Official Secrets Act is involved. But I do have something for you in the public domain.
Quick question though - did the STASI spy on NATO countries? Yes. Was their primary mission domestic control and keeping tabs on the domestic population? Yes. Is it reasonable to think that the UK/USA spy agencies were any different? Did they spend time monitoring the Soviets? Yes. Did they spy on Arthur Scargill and the miners? Yes. What about Greenpeace? Yes. Fundamentally the miner's strike was an existential threat to the ruling elite whereas the Soviets weren't ever going to invade. Hence the mission creep.
Furthermore, if you do have mates from school days that do work there and, after plying them with lots of alcohol in an effort to find out more, you soon realise that they are all working in isolation, not knowing much about the big picture. There are only 'tells' such as their reason for doing the work. Yet amongst the tells a picture emerges, for instance overall capabilities or that your friends aren't actually working on the things in the mission statement. For a while the war on 'kiddy porn' was an acceptable reason for working there alongside fighting organised crime and The War Against Terror.
But when you examine these noble efforts you soon realise that a little bit of a fig leaf is being presented. GCHQ are not the ones unearthing the Panama Papers, the 'kiddy porn' mission ended up becoming regular police work rather than what the UK needed GCHQ for and then The War Against Terror certainly was not anything that the public were led to believe, despite the public diplomacy that existed at the time regarding 'intercepted intelligence chatter'. Now is not the time for in-depth discussion on this latter aspect, however, you can check how 'intelligence' was gathered during the war, for instance the 'Dodgy Dossier' that Tony Blair prepared for Iraq, that was based on some paper found in the public domain by Number 10 and 'sexed up a bit'.
So, on to what is available in the public domain. A good place to start is with Duncan Campbell, the investigative journalist that brought knowledge of ECHELON to the world. This is now a long time ago and very much from the Cold War. The report made for the European Parliament is a very good place to start, here is a little overview of that:
http://www.europarl.europa.eu/EPRS/EPRS_STUDY_538877_Affaire...
If you then dig a little bit deeper and read the testimony of whistleblowers that spoke to Duncan Campbell you will find that there is much to support my assertion. There is one story that almost made daylight concerning Menwith Hill, a listening station that was supposed to be pointing east. There weren't Russian voices coming in over the ether, however, there was the voice of Strom Thurmond, a big believer in the war machine and a congressman definitely in the pockets of the arms companies. Despite this GCHQ were doing the listening for their counterparts on him, who was as trustworthy as you could have wished for and definitely not a Soviet asset.
In war you do not have complete information and reliable sources of what is going on in other people's kitchens. However, if you study what is in the public domain and do a little bit of asking around then you can get a glimpse of what is going on. History is important too, with the UK there is the former empire and the 'Special Relationship', both shaping what the doughnut is really about.