Hi chaps.
What your getting is a back feed spike from the liesure battery via the alarm system.
The caravan builders are too lazy to put a seperate permanent live from the 12v input to supply the radio seperately. What they do insteadis patch into the caravan alarm permanent live. When you interupt this with another supply like that from the car, or the leisure battery voltage drops below 10.5 volts this is detected by the alarm system which even when turned of, sends a signal. This electrical impulse is enough on some radios to switch it on.
So all you have to do is find the permanent live connection, disconnect it and fit a new wire fused of coarse, from the leisure battery to the radio and hey presto, no more ghostly goings on in the radio department.
Cost less than