Rover 216 1590cc petrol auto 1991 oil light problem?

My Oil light comes on and stays on when the car gets warm (10 mins) I've had the oil light switch on the engine changed and it still does it. Is my engine pressure low and if so will changing the oil and filter fix the problem? I don't believe this has been done for some time. If it is not the answer to the problem, then what will fix it, a new oil pump? If so where would I get one at a reasonable price?