Not sure about this one.

My fabia has recently started whining when driving normally. I don't think it's a bearing going as the pitch is constant - around 1kHz, regardless of the speed. Also, it appears to whine more when turning in one direction than the other.

I think I'll take the wheels off and make sure the pads are properly seated and it isn't a small pebble which is vibrating causing the whine... Visually, the outside of the discs look fine.

So apart from that, any suggestions as to what it may be?

I'd say pads or calipers. My MR2 did a similar thing and it was the anti rattle clips. They just needed bending a little.