You don't state if it's a combination freezer/fridge and if it is, whether it's a side by side or over/under.
If, as you say, it's freezing the things on the fridge side, let's assume it's a side-by-side and the freezer side works fine. If that's the case, it's likely the airflow control mechanism between the two sides is not working. It's usually (depending on brand) a small door affair at the top of the wall between the two compartments. It's controlled by the thermostat one sets for the fridge side. It's usually fairly inexpensive to replace and can be done by an astute DIYer.
I'm in the U.S., but here's what one model looks like and the cost...
http://www.repairclinic.com/SSPartDetail.aspx? s=t-SRD27SRW-%3d%3dc221i237368&PartID=237368
Keep in mind that here's usually only one source of cold air to both sides, that being from the compressor to the freezer side and then shuttled to the fridge side.
You could, when the unit is running, simply hold your hand up to the vent and see how much air is moving versus turning the thermostat up (higher temp) by comparison.
I've seen some models that has a small metal lever that attaches the described vent to the electrically operated motor that modulates it. Sometime this lever can be easily detached and the door moved by hand until you can get it replaced...
Good luck!