That doesn't sound like the statement of someone who has actually checked to find out whether any surveillance was conducted. It sounds like someone making a rote denial based on the assumption that any such request would be denied according to their understanding of British law. But that's simply not how intelligence agencies work. First, any such request would undoubtedly be framed in national security language ("Look, we can't spy on a presidential candidate. It would look bad. But we think this guy has Russian connections. We need you to spy on him -- using the NSA's infrastructure but you originate the request to get around US law -- and give us the take so we can make sure this guy isn't a Russian plant"). Second, such agencies basically ignore the law, since no one is willing to enforce it against them. They use national security law against others, they don't follow it themselves. And third, they don't report on their requests and operations to random government officials who are authorized to confirm or deny such requests to press inquiries.
If in fact the Obama Administration made a request of GCHQ to access the phone calls of his advisors, there are probably three people at GCHQ who know it happened. That's the person who received the request, the person who carried out the request, and at most one level of management to authorize it. And none of them are likely to be talking to the press.
In fact, the article I quoted above is probably best understood as a veiled threat. Shut up and don't admit to anything, or we will prosecute you to cover up our involvement. Sound familiar? As always, if you or any member of your team are captured or killed, the Secretary will disavow any knowledge of your actions.