To be honest, what you've said is unfortunately the conclusion I've been slowly coming to given there seem to be no obvious issues with insulation, etc. However, is 13.5 degrees at around 8am really not that unusual in a 15 year old extension in October (with no heating on)? I think my main confusion is that it is 3 degrees colder than the 140 year old solid walls in the rest of the house - my uneducated brain just tells me something must be wrong!
Where is the room thermostat located, can it be moved so it uses the temperature in the extension?
Are TRV's fitted on any/ all/ some of your radiators?