This is a hot topic for me. I fly large model gliders (around 10ft wingspan).
In order to fly them at any recognised UK, I need to be qualified and have passed a practical flying test and be insured (25 million per claim). This is organised by the British Model Flying Association, who manage and monitor model flying in he UK. Anyone attempting to fly a traditional model without a qualified instructor is unlikely to have a model to fly for many minutes.
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These drone are very simple to fly and even the largest could be flown by a child. Very few owners/flyers are qualified or tested in any way and many have no appreciation of the risk they are taking. (or care ) They also have an extremely long range, way beyond the ability to see them.
The solution would be that all model flying would require insurance, that would bring all model flying under the BMFA, requiring insurance, tuition testing and qualification.
The existing BMFA test includes safety, on the ground and in the air, rules covering flying sites, flying near areas of population, airports etc, equipment checks and safety along with a practical flying test that demonstrates full control of the model and the ability to recover from emergency situations.