If GCHQ are involved with any such interference, their actions are fairly unconstrained by law. Paraphrasing Intelligence Services Act 1994, s.(3)[1]:
> [GCHQ shall] monitor or interfere with electromagnetic, acoustic and other emissions and any equipment producing such emissions [...] in the interests of national security, [or] in the interests of the economic well-being of the United Kingdom in relation to the actions or intentions of persons outside the British Islands [or] in support of the prevention or detection of serious crime.
As far as I know, there is nothing in statute that constrains how they go about that (Regulation of Investigatory Powers Act 2000 adds a couple of hurdles in regards to interception). Any oversight comes from various Parliamentary committees.
[1] http://www.legislation.gov.uk/ukpga/1994/13/crossheading/gch...
He might work around it but it's an option. I don't know about whether it's legal under UK law but their surveillance organizations seem to get away with a lot.