And if the pipe is easy to access to repair then it should be straight forward
For a fridge engineer. you'll need manifold gauges, a line tap valve, a vacuum pump, oxygen free nitrogen and refrigerant. Plus probably brazing kit. I reckon £100 worth of repair.
Adam is right, it's probably lost its gas. The weakest area on domestics is the capilliary tube (very small bore pipe). It acts as an expansion valve and leads into the evaporator (cooling coil on the inside). Even a cable can rub through these. You want to check that the evap is completely clear of ice before calling anyone in though.