Oh don't get me wrong, it was a complete mess - for all of the reasoning they had they then felt unable to let any of them go out of business and spread the work too thinly. I think your idea of having English Electric and GEC, assuming that Vickers was busy carrying out work for the Admiralty, as central project managers has a lot to recommend it. Britain had a habit of having too many firms in an industry - aerospace, computers, automotive manufacturing, shipbuilding etc. - that meant they were too small and the markets too fragmented to compete with larger, often foreign, companies. That's why I've generally advocated that they should have gone for what I usually dub a 'twins' strategy - encourage consolidation in the various industries so that you end up with a pair of large companies - e.g. Hawker Siddeley and BAC, EELM and ICT, Leyland and BMC etc. - that are better positioned yet doesn't leave you with a monopoly situation and encourages competition.
Standardisation would probably have helped as well. Considering the links they had early on I've sometimes wondered what might have happened had the UK and Canada maintained closer nuclear industry links. With hindsight helping contribute to the partnership that eventually developed the CANDU reactors would have been a smart move as a potential back-up/alternative.