It's not even just the money.
My wife works for the German civil service, and according to her, the pay there is also crap. But it's not all quite so cut-and-dried.
There are plenty of people working for the German civil service who are, actually, quite happy - despite earning €25-35K. The main reason for this is that they have a different system of employment - once you have been offered a position as beamter, it is practically impossible to lose your job.
(Of course, it's not impossible, but the costs involved in getting rid of a beamter mean they're practically bulletproof to all intents and purposes.)
This means, essentially, that you trade salary for job security. This isn't just a benefit for you in terms of peace of mind, either - it's actually a valuable benefit if you ever apply for a mortgage, because your low-risk status is officially recognised, and it gets you a cheaper interest rate.
However, working for the UK civil service offers you zip in the way of job security or actual benefits, beyond the warm glow of actually getting the Queen's birthday and half of Maundy Thursday off. If some beancounter bleats about costs, you can still be axed - just as easily as anyone in the private sector - and you'll still be out on your ear.
Then there's living costs: My wife and I pay 664 euros per month for a nice flat (~60 square metres / ~646 square feet) in a good area of Duesseldorf, with excellent access to public transport. (It's so good, in fact, that we gave up on car ownership in 2009 and saved ourselves a packet.) Unlimited public transport in the city will cost you 65 euros per month. If you had to live on a civil service salary, you could still be left with more than half your income - after tax. The bottom line is that you can live a reasonable life on a low salary, here.
But the UK? You have no reasonable public transport, other than in London, which is so expensive that it makes Tokyo look like a bargain. Your road system stinks, and running a car in the UK is getting prohibitively expensive. You'd also be lucky to rent a room in a shared house for what you could get a whole flat for in Germany.
This is why I think GCHQ are stark, staring bonkers if they actually expect anyone intelligent to come and work for them for £35k, a pat on the back, and a few extra days of leave (which you can't do anything with anyway - because you'll be so skint that you'll be staying at home.)