HDMI Cable interfering with mobile phone network
Ok, first of all, that wasn't an OFCOM official, probably, in all likelihood. Best case, you just failed some security penetration testing.

Other than that, if the guy with the directive antenna, proper spectrum analyzer and training says "that's where the radiation comes from", I'd trust him.

HDMI symbol rates are, depending on HDMI generation used, 165, 340 or 600 MHz, meaning that at these frequencies or typically odd multiples thereof, you'll see harmonics, with power strongly decaying with the multiple.

UK uses cellular bands at 800, 900, 1400 and 1800, 2100, 2300 and 2600 MHz; aside from the unlikely 600 MHz·3 interference, those are not likely victims.

Then again, OFCOM does have a phone number for spectrum interference investigation: 020 7981 3131 (option 2); so ask them whether someone was dispatched to your location. It's a legitimate concern.