I did a little digging. In the states we use a thermostat called a jumpstart as a low cost solution to controlling heating pads and the such.
I found one on Amazon UK that is the same type with the crazy style plugs you Brits have
https://www.amazon.co.uk/ROOT-T-Ther.../dp/B00I3C9DEQ
This will get your heating under control. Heat pads often called undertank heaters are the most common controlled by these but with the woooden cage type that is popular in your country, I am not really sure what to offer aside from overhead heating. I assume you have a wire guard around the lamp bulb. If so you could always switch to a ceramic heat emitter and use the above thermostat to control it. You would place the probe inside the cage under the ceramic emitter and plug the emitter bulb cord into the thermostat.
This is an example of a ceramic heat emitter. It does not produce light so you cna keep it on 24/7
https://www.amazon.co.uk/MvPower-Cer.../dp/B00QGITSBM
This is an example of a wire cage that should already be in the enclosure that protects the snake from coming into contact with a heat source
https://www.amazon.co.uk/Repstyle-Ro.../dp/B008184RJ8