Could be a fault in the electronics of the airco anyway. Don't be surprised when u turn the airco off for example in an Alfa Romeo and it still would be running.
But if it is the air flow(cold air is more dense so it really makes a change) and you want to install an open racing air filter,make sure you install a tube that brings cold air to the car. I did that modification on a 33,first without cold air flow and then with,and it really makes a huge difference in performance. Ofcourse it wont help much when you are driving slow.
Forgive the poor English language but I am not British.