Over 90% of UK registered aircraft are GA, and they only account for one third of serious losses of separation. Two thirds are down to professional pilots using ATC in Controlled Airspace.
That statistic you make about UK GA also takes no account of the many aircraft which transit the UK each day, or are based here under a different State of Registry. Do UK GA aircraft represent 90% of all the UK movements ?? I doubt it. The GA in the statistics will be for all GA which are involved in a serious loss of separation, regardless of where they are registered.
You can't say either for certain that all the rest are caused by professional pilots. ATC make errors too, authorities make errors, operating agencies make errors. The list is endless.
All you can say is that statistics can tell you whatever you want to hear.
The real fact of the matter is that an infringement of CAS has the potential to result in a mid air collision. Fact. It will only take one, and should that ever occur (God forbid), then you can expect GA in the UK to be severely restricted and penalised in a classic case of bolting the stable door after the horse has bolted. One collision may have been seen as unlucky, but two will place the authorities in the realms of negligence if they have not taken measures such as mandatory surveillance equipment and other technologies to prevent it reoccurring. So they will use a very large sledgehammer to crack the nut ... and GA.