GCHQ is signals intelligence, so if he was tapped, it was probably by GCHQ. But let's face it, he wasn't, Trump is an imbecile that is just parroting right-wing media accusations.
You kind of have to wonder if Trump is even aware of the implications and consequences of what happens when POTUS spouts off completely unsubstantiated conspiracy theories. You have to wonder if he fully groks that he isn't "just some rich guy" any more.
Why - doesn't GCHQ do SIGINT and SIS (AKA MI6) does HUMINT?
NB I don't think they did snoop on Trump, but if anyone was going to do it from the UK it would presumably be GCHQ.