Does it ever get that cold in the UK? You should have a northern US winter 'cross the pond. That'd thicken your blood right up...JK
Yep, the head gasket would be unlikely, and fairly easy to diagnose with a compression test. Bleeding is far more likely. I use a few rules of thumb when working on my cars. This one is a cardinal rule...if some system I just worked on isn't right after I've been there, I suspect that immediately. Sounds simple, but I've ignored it many times and suffered great frustration.
My overheating problem was cheap & easy, I hope yours is the same way...about $15 for 4L coolant (BMW makes great stuff but I used Zerex G05 this time), $9 for water wetter, $3 for 4L distilled water and $10 for three new bleeder screws. Never know when you'll need another, eh? $39 is pretty good, I was really worried about it until I got it buttoned up. The big cost will be the valve if that's your trouble.
Your e36 compact has the single temp HVAC, right? They all did over here. That's a lot easier than the dual-temp system with the little valve servos controlling the temperature. The diagrams at RealOEM will detail your exact system setup.