And you bet the CAA prosecute illegal use of frequencies causing interference with legal users.
They will have to notice it first, which they won't. Every radio frequency has tons of interference on it, here and there. A private strip will have hardly any use at night, and it is a piece of cake to find a frequency not used by any known airport; there is a website listing allocated frequencies for the UK and probably Europe.
Not suggesting anybody does this though, because there is little point. Google on
sms remote control
and you will get the idea. There are loads of products and sms does work at low altitudes. It takes very little interaction with the phone to do this; just store a template message in some folder and send it when you want the lights on. I have such a box right here, enabling me to control the ADSL equipment at a remote location, to reset it when needed. It cost me about £200 and that included adding a big relay to switch a higher current than the built-in one.