Sounds like similar symptoms to what I had on my old engine. Pushed coolant out the top of overflow bottle when it was at the Ring, bit of bubbling in there too, and the temp needle when up high during a lap. Only had an issue on track on hot days (I'm guessing it was pretty warm at Snetterton yesterday!)
Not sure I ever got to the root of the problem on it though. Worth getting it sniff tested, mine came back OK. I changed the radiator, thermostat and a few other things and did another full day at Bedford and no overheating issues, but ambient temperature was much lower than a hot summers day. So not conclusive either way.
My original radiator at 14 years old was knackered - I swapped it out in 2016. All the fins were turning to dust and flaked off if you ran your finger down it. I guess your hawk will be at that same age now if you're still on the original rad. Not sure how much the radiators efficiency drops when its like that but it can't help. Worth changing if you haven't already.
This was my old one: