I don't think it's easy to place blame on any single part of the NHS's organisation for the way events and circumstances have evolved and left us with such apparent chaos and long waiting times we seem to be seeing.
The provision of Health Care across all settings is a very complex set of procedures, and successive governments have all failed to fully understand the extent and cost of providing what we have come to expect.
When the NHS was created in the 1940's the population had a very different demographic, to today, and the expectations of the public were also very different. In practice much of the medical knowledge was still fairly primitive, and the Dr's may have had a name for a condition, but they didn't necessarily know how to proactively cure it.
One of the strengths of the NHS was it had the critical size and funding to start more research and to produce better outcomes for many conditions, but it also means it has now identified many more conditions which through developments it can now treat. This has widened the scope of the NHS and as is so often the case these new procedures and medicines all add to the cost burden on the NHS. And it has increased the public's expectations of what the NHS might be able to do.
A&E and Hospitals are just steps in the critical healthcare system,
and they are dependant on systems and procedures outside of their direct control to allow them to function effectively. "Bed blocking" is often cited as being a major restriction for the admission of critically ill patients. This is where the hospital is not satisfied the discharge route for a patient has been properly facilitated to receive the patient with their post discharge needs. This process actually falls on the local authority over which the hospital has no directive control.
We also have to recognise the demographic of the population has changed, partly due to the success of the NHS, the UK population as an increasing number of older people and as anyone ages they are more likely to need medical help so the burden on healthcare is increasing.
As Oc has pointed out the social care system (again local authority based) needs both a massive injection of funding and a more cohesive management that can quickly bring the necessary resources and support to meet post discharged patients short and long term needs.
Whilst these would be great interventions, there are still other needs to be addressed to bring down the pressure on the A&E and hospitals in terms of the numbers of minor conditions that present at the emergency departments rather than being handled more effectively by local service distributed across the population such as GP Surgeries, Pharmacies, heath centers, or even minor injuries facilities. locally, rather than centrally.