Strictly IMO, where the UK ran into problems was that they continually tried to leapfrog generations of aircraft instead of building successive generations and learning from the experience gained. Granted, they had good reason to at the time. Aircraft were advancing so rapidly that they knew they couldn't afford the more deliberate approach.
As an example, in 1953, the subsonic, gun armed F-86 Sabre and MiG-15 were state of the art, front line fighters. Just five years later, the Mach 2 missile armed Phantom (and nearly Mach 2) MiG-21 were both flying. The UK didn't have the funds to do what the US did and field hundreds of fighters of each successive generation. They could field hundreds of modern fighters only if they were able to build fighters that essentially skipped a generation of development, giving them a leg up on everyone else.
Unfortunately for them, they bet the farm on this plan and it backfired. Hard. From what I can see, mainly for two reasons: trying to sustain multiple companies and finding development of too many designs instead of focusing on just a handful. And badly guessing when aircraft technology was going to leap forward. The first problem could have been solved had someone actually used a little critical thinking and narrowed down the proposals too just two or three designs earlier instead of trying to keep ten different companies alive by funding their prototypes, and then not having the money to actually buy any of the proposed jets. That also ties into my second point:
They spent so long evaluating proposals trying to sift the wheat from the chaff that by the time a decision had been made, aircraft technology has moved on and left them with a substandard design, forcing them to start the whole process over again. And in the few cases where they did get an aircraft into service, the tech jumped immediately after, leaving the UK with a whole lot of brand new, very expensive and totally obsolete equipment.
Now, obviously there are exceptions to this. The EE Lightning, the Jaguar, the Hunter, the Harrier and the Canberra spring immediately to mind. But overall, the UK was never able to make this strategy pay off. And in the long run, it cost them the ability to independently design and build their own aircraft