The only way the system could be changed in an attempt to achieve the effects you desire are by instituting a National College of Aviation and by outlawing all UK speculative commercial training schools. However, as we are part of the EU, graduates of any JAA schools in Europe would be entitled (as they are now) to apply for any jobs available in UK. The airlines may not discriminate in favour of UK applicants, so we would find a greater proportion of UK-based jobs going to non-UK graduates. Naturally, those UK wannabes who couldn't get into the NCA would take their money to the plethora of schools that would inevitably spring up in other EU countries in the hope of bypassing the system.
What would all this achieve? The closing down of several dozen legitimate businesses in UK and the increase in cost to UK wannabes who couldn't get into the NCA. However, you could have a centre of excellence that all schools could aspire to; however, that would depend on how it was funded.
What other ways could be tried? I'm not sure, really. If you attempt any legislative remedy that only applies to UK students or airlines, you'll force people to go elsewhere. If you attempt an EU-wide legislation, you are effectively advocating a return to centralised, government-controlled training which, by definition, would we unwieldy and slow to respond to fluctuations in the market. It won't happen; we've been there (in the days of nationlised airlines' own schools, and reliance on the military for the rest) and and it would not work in today's circumstances.
I would love to be able to force airlines to make greater efforts to predict their pilot requirements over the medium term, and to contribute towards a training system that provided the majority of that demand. I just don't think it could work; airlines' (and governments') predictive powers are bloody appalling, and they will do everything they can to avoid unnecessary expense. Nor can you force the schools in the open market to stick to a certain proportion of the overall pilot supply cake - market share is what they all fight for, and they will not appreciate that market being manipulated by legislators.
One thing we could do ('we' as in the JAA countries) is to make it compulsory for all training to be to a common level, as well as a common standard. Say to MCC. However, that might mean the end of modular training. Then make it compulsory for all airlines to be financially responsible for all training thereafter - though that would inevitably mean a deterioration in initial salaries for new pilots, and would not necessarily get rid of the pay-to-fly brigade.
Scroggs