Recruitment isn't a problem if there is a worthwhile mission. Things like the Berlin Airlift and Marshall Plan motivate people.
The idea that GCHQ is doing anything other than preserving Britain's role as junior partner in an increasingly immoral American empire is kind of laughable.
At this point, what do America and Britain stand for?
That and a lot of the people with the genuine skills they need are actually on the other side of the spectrum from them on things like liberty, free speech and privacy.
A large government department requiring niche technical skills on public sector pay and bureaucracy levels in a rural part of the country?
There are probably some difficulties.