So, the guys at NOG just gave me a call and it turns out that the valve clearances were very tight. So tight that you couldn't get the gauge in there!
The last service (done by the previous owner) wasn't a BMW dealer and I can only assume that he either hadn't checked or was overzealous. That being said, I've ridden it a 2/3 thousand miles since I bought it. Can they tighten up over time? 
All in, because of all the time it took them to work it out, it's gonna cost me £150. Not cheap for doing the valve clearances... but at least it's taken care of and I would've had no idea working on it myself.
Yet another top job from NOG

All in, because of all the time it took them to work it out, it's gonna cost me £150. Not cheap for doing the valve clearances... but at least it's taken care of and I would've had no idea working on it myself.
Yet another top job from NOG