It's pointless comparing the gun laws and shootings between the US and UK.
The UK was never "frontier territory" where a gun was an important tool. We didn't have civil wars after modern guns were invented. Gun ownership has always been relatively rare so "controlling" it was simple and easy.
Any solution that involves magically disappearing all guns from existence is pointless to debate. Why not also solve it with magical invisible nano-bot bullet shields?
Assume any solution has to align with people having the right to own guns and work backward from there. The problem isn't really people having access to guns, because people have access to guns in lots of places, and there are not the same mass shooting incidents. Likewise, if guns used are already owned illegally, making more laws to make them even more illegal isn't going to do much.
Look at who does the shootings, why, what warning signs existed, who could & should have noticed them, who did but didn't act, and which politicians stand to benefit from mass-shooting events.
Who makes hay when the bullets fly? Who stands to gain? Who sets what policies and why? Who stops criminal accountability?