It's probably not a good idea to stand outside GCHQ's fence and take photos. They'll claim it's to protect secrets - the privacy and secrecy of who works for them, for example. (Because there is mostly carpark between the doughnut and the public road). I don't know if someone would get arrested, but "they" would certainly feel able to use their anti-terror powers and the experience would not be pleasant.
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In England there's the Official Secrets Act. Signs say something like "a prohibited area as defined by the Official Secrets Act".
There has been some paranoia around photographers taking photographs in public. The London police force had to issue guidelines for their officers about correct procedure. (http://content.met.police.uk/Site/photographyadvice) (http://www.bjp-online.com/british-journal-of-photography/new...)
It's probably not a good idea to stand outside GCHQ's fence and take photos. They'll claim it's to protect secrets - the privacy and secrecy of who works for them, for example. (Because there is mostly carpark between the doughnut and the public road). I don't know if someone would get arrested, but "they" would certainly feel able to use their anti-terror powers and the experience would not be pleasant.