|Thames House - MI5 HQ|
This clearly needed further investigation. After some extensive research (I Googled MI5!) I found their, quite comprehensive, web site, and sure enough they have a recruitment section giving details of their requirements for a variety of jobs within the service.
Should MI5 not be your cup of tea,(or vodka martini) there are links to the sites of MI6 and GCHQ, so surely there is something in there for everyone.
I would imagine that the rejection rate among applicants is pretty high, but you never know, a new, fascinating, though potentially short, future may be there for the taking.