1987 Cab is whirring?

My 1.8 1987 cab is whirring. I am not experianced with working with cars and i am trying to fix the problem!
The way i would describe the sound is like a remote controled car. You cannot hear the sound when you start up the engine but it slowly becomes louder. The sounds becomes louder when you press the accelerator
I have no power steering or aircon.
I have changed the alternator and the belt.
I have taken the belt off and started the engine up and it still whirs, so it is not the water pump.
Any help would be very appriciated, I love the car but cannot pay/have the cheek to get a garage to look at it.
Thank you

Does it alter pitch with engine speed?

Sounds like it could be the cambelt being too tight, but in my experience you usually only get a whirring noise  at idle speeds (or around that kind of speed) and then it disappears when you raise the revs.
You could also be on the verge of a cambelt tensioner failure, so that would need to be investigated.

Maybe you can upload a short video to photobucket or suchlike so we can hear the sound ourselves, otherwise we're just guessing.