Thanks for the extra thoughts Aaron, I await a hot summer UK day when I'm actually away to test everything properly.

Back to the butane v propane experiment, I have concluded the following:
1. There is nothing basically wrong with my fridge. It works as expected on 230Vac getting down to 5C with the thermostat at approx half range.
2. Using propane and the on-board 30mbar regulator the fridge will only achieve 11C on the mid setting and 6C on the high.
3. Using butane and the on-board regulator the fridge achieves 6C on the mid setting and less than 4C on the high (I stopped the test after 4C)

I have now purchased a clip-on butane cylinder convertor and a butane regulator pig tail and will be exchanging my propane cylinders for butane as they run out. I'll keep one propane in case I start the season very early as I did this year.

Last resort, read the manual

Three points of interest from the Dometic manual for my RM4230 fridge, manual dated 06/2002.

1. "If the refrigerator is not cold enough it may be because..." Various normal faults plus "The gas pressure is incorrect - check pressure regulator at the gas cylinder"
2. "The refrigerator is designed for operation on LP gas of Butane type the pressure of which must be 28 mbar for Butane and 37 mbar for Propane" The standard bulkhead regulator is set at 30 mbar, nearly 20% lower than that recommended for Propane.
3. "On LP gas operation lighting should always be initiated with the knob at the max position. If the ambient temperature is above 25C and/or the door is frequently opened the knob should be left at that position. Below 25C the knob should be set at mid position and below 10C at min to avoid temperatures below freezing in the main compartment" This is pretty much how I found the operation on Butane to be.

Conclusion: Whoever decided that 30 mbar should be the standard for caravan regulators have condemned these refrigerators to inefficient running on Propane.

Now I know