96 Astra with ABS - Noise on Wheel Rotation

This one has me stumped.
1996 Vauxhall Astra 1.4i fitted with ABS.
The car has started suffering from a slight rubbing noise which can be
heard at low speeds and is speed dependent. It sounds a bit like a disk pad or drum brake shoe rubbing against a slightly out of true disk/hub or something rubbing against a wheel or tyre.
The noise can only be heard when in the car (seems to travel through the bodywork making it difficult to pin down the source) and seems to be once per wheel revolution. Applying handbrake or footbrake makes no difference to the noise.
All wheels turn freely when jacked up although the rear offside you can hear a very slight rub on the shoes once per revolution. Checked & cleaned the drum & brakes on that wheel.
I tried braking the car gently on a downhill stretch of a quiet road and found that turning the ignition off stopped the noise. Turning the ignition back on (but not starting the engine) caused the noise to reappear.
ABS warning light comes when turning ignition on & then goes out a few seconds later just as it should. No warning lights on the ABS when driving and no trace of vibration/kickback is felt through the brake pedal.
I have tried a few more things and the symptoms of the regular rubbing noise seem to be as follows:-
Drive the car with withthe ABS fuse pulled out - no noise
Set off slowly forwards - initially no noise until wheels have turned for approx 1 revolution (or car reaches the speed when the ABS activates?) then whirring noise (ABS pump running?) for about 1 sec followed by noise once per wheel revolution.
Drive the car round a car park & noise seems to stop when turning left or right, Also stops when going round roundabout.
Noise is the same whether braking or not.
Car passed it's MOT test with no problems or advisories although the noise seems to be louder now - MOT brake test has allowed the rear brake auto adjusters to tighten things up a notch?
Could it be that the noise I am hearing is actually the ABS pump running regularly? If so, why would it stop when going round corners?
Any suggestions gratefully received.
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kevman wrote:

first would be a clean up of disc pads and calipers with the right grease on all sliding bits, check for any wear on the discs too, a lip at the edge can make all sorts of funny noises. Ensure the caliper pistons move freely too. A set of genuine pads and discs are very cheap if there is any doubt over condition. While you are there check that the hub nuts are tight.
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