MI6 (Secret Intelligence Service) UK
'My name's Bond. James Bond.'
The original character for Ian Fleming's James Bond worked for Naval Intelligence, which is where Fleming himself worked during the Second World War. (Check him out on Wikipedia – it's an interesting story).
In the modern UK, active human based (as opposed to radio / signals) intelligence gathering on foreign countries (ahem, cough, aka 'spying') is carried out by the Secret Intelligence Services, popularly known as MI6 (the former Military Intelligence Section 6). It is the nearest UK equivalent to the CIA.
Until 1994 the very existence of SIS was 'secret' and recruitment was done by taps on the shoulder in the 'old boys' and 'old girls network' – you could not directly apply for a job. As the various intelligence debacles of the 40s, 50s, 60s and 70s showed, that system did not always work.
SIS has moved to a more open structure and much wider social recruitment (I don't think they really care if you prefer your martinis shaken or stirred), and the website (https://www.sis.gov.uk/) is part of that new approach. From 2006 interested applicants were invited to apply directly for jobs.

The website gives a quick tour of SIS and lifts the veil a little on what until recently had been a state secret.
For British citizens checking out the SIS website you can also apply online for a career as an 'operational officer'. (The word 'spy' is never mentioned!) Of course, as soon as you apply, the 'vetting' process will start, so if you hear clicks on your phone or see someone watching you… (!)
For those interested in more detail than you can get from this website, a couple of recently published history books should get you started:

MI6: The History of the Secret Intelligence Service 1909-1949 by Keith Jefferey

and

Inside British Intelligence: 100 Years of MI5 and MI6 by Gordon Thomas