Good advice from buildersmate, but with one addition. Unless refrigerators are totally different in the U.K. than here in the U.S., there's really only one source for the "cold". The compressor, as mentioned, produces the cold which is circulated in the freezer side by a fan. There's an opening between that compartment and the refrigerator side through which the cold air passes. To keep that side from also becoming a "freezer", the passage way is restricted or controlled by a device called (here, at least) an air damper assembly. This is usuallycontrolled by an electric motor or solenoid that responds to the thermostat on on the 'fridge side. This is probably the culprit. It can be changed out by a reasonably astute DIYer, but finding the right part number can be daunting. It shouldn't be too expensive and at least the potentially costly parts seem to be working, i.e. the compressor as mentioned... Best of luck!