High-pitched rubbing sound when in gear

Here's hoping someone will be able to diagnose this!

My 2011 1.4 TSI has developed what can only be described as a high-pitched rubbing sound. It's only present when the car is moving and in gear (whether under power or not), but disappears when the clutch is down or in neutral. I first noticed when engine braking, as the sound kicks in when you lift the clutch.

The sound is throbbing/cyclical, and speeds up as you go faster. I'm inclined to say it's tied to the gear, as the tempo seems faster in a lower gear at the same speed (though I admit that could be my imagination).

I hope that makes sense. I'm also hoping this isn't going to cost me a fortune!