Hello Matt,
Not sure if I can help you. Last sentence - sorry, it doesn't make sense to me, but it could be me.
Could I start by just clarifying that this noise is not there when you rev. the engine at standstill, but only there when the car is moving? If only there when on the move, have you tried (under safe conditions) to deviate off a straight line - to the left and right - when this noise is present to see if the noise gets better or worse? Does the noise vary on cornering?
Warped discs? I would not have thought so, since you would be more likely to feel a pulsing of the brake pedal.
You seem to have eliminated the tyres, which is always the first port of call, and this may narrow it down to a wheel bearing, or if not that, possibly a drive shaft issue.
Kind regards,
Gareth.