By way of comparison, GCHQ personnel seem to be leaving for 4-5x salary from big tech companies[1]. So do the math and figure out what the GCHQ folks are being paid.
Also, GCHQ has hired 494 contractors for 71m GBP[2].
I live in Cheltenham and pre-Snowden may have entertained the idea for working there. I tracked a job they were advertising for nearly a year - they were offering ~32k for a Linux expert with years of experience. Good luck on that one. I think they eventually converted it to a contract role, but even then I wouldn't entertain it.
Another friend worked at the big James Bond building in London, was regularly taken around the world at short notice to do security things, and was on less than 40k. He loved that job more than anything in the world but literally couldn't afford to live there so went contracting for 5x the money. Apparently in the government a large part of salary reviews is based on (age + seniority), so you're waiting a long time for a decent uplift that may never arrive.
Also, GCHQ has hired 494 contractors for 71m GBP[2].
[1]: https://sites.google.com/a/independent.gov.uk/isc/files/2016..., page 40
[2]: Ibid, page 70