It could be as simple as the earth being absent from the lighting circuit and your meter being very sensitive/high impedance. Upload some photos, for a decent opinions.
As above, though just a slim chance that the 240v is from the radiator - check for voltage between switch screws, and 13 amp socket screws.
The above almost covers the tests required to determine what the "fault" actually is.
Purchase (or borrow) a cheap low impedance analog multi-meter. (or, Shunt a high impedance digital multimeter with a 10,000 Ohms resistor.)
Use this to test for voltage between
1. the screw and a "good" Earth, (which should be available at the Earth pin of a 3-Pin Socket-outlet - or any Earthed metal object plugged into such a socket. (e.g. A toaster, iron etc.)
2. the metal radiator and the above-mentioned Earth.
3. the screw and the metal radiator.
All should read (almost) Zero.
If 1 reads "High", the fault is in the household Earthing to the "box"
If 2 reads "High", the fault is an incorrect electrical connection to the radiator piping.
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