There's a thermocouple switch which activates the fan when the coolant in the radiator gets above a certain temperature. It's probably the switch, which is cheap - a new switch is probably all of £10 including delivery.
Installing is relatively simple job, but IIRC the sensor on Corsas is typically at the bottom of the radiator, so you would have to get under the car and deal with the coolant coming out. Draining the coolant is the normal procedure, however you could get away with not doing that if you are quick with your thumb and have a bowl and towel handy - you get the old one off then cover the hole, then get the new one on quickly. Afterwards you replace the coolant lost in the process, and makes sure any air introduced gets out of the system.
Given it's a certain amount of trouble to do that I'd suggest you check the contacts on the sensor and the socket as well as the wiring continuity before you take that step.