This sounds like the thermostat has failed, and the fridge thinks it hasnt reached the required temp.
Firstly its worth checking the fridge super cool \ deep freeze setting hasnt accidentally been switched on (though it should deactivate automatically), secondly its worth doing a de-frost (even though the fridge should do this automatically as well).
If after the fridge has defrosted, and then switched back on your seeing a build up of ice and the fridge is not responding to the temp control, its time to treat it as a hardware fault.
A new thermostat is around £15 from here, these are not the easiest to replace so would suggest you have an engineer do it for you, if your not careful you can end up damaging the insulation or crack some of the plastic mountings which you need to remove to get to it.
If you would like me to recommend someone, please provide your post code, should you have any questions or need anything clarified, please let me know.
Hello I am just following up from last week, do you still require assistance, if the above suggestion has resolved your issue I would appreciate if you could rate the service received.