I went into A&E on New Year's Day myself (with a relative, not for myself), after noon. The waiting room was packed. I don't know if it was typically/atypically busy for a NYD, a Sunday, any day at all, not being a regular there. But I didn't detect any undermanning (if there had been more staff there might have been less room for patients!), SFAICT it was just a demand spike, possibly with some less urgent cases than those fireworks-related ones (possibly including my relative, who got a night in their wards regardless, and a further couple of nights since "for observation"). Not brilliant (the hospital, that is; the bit about the relative goes without saying...) but neither was it exactly a war-zone.
I feel I must point out that when there's a lot of people using a service, even an admirably low rate of 'falling through the cracks' or otherwise succumbing to random unforseen events can manifest itself in notable examples. But this makes it no less a tragedy for anyone who finds their relative becoming such a notable outlier.
I also must point out that at least one hospital in the region (not quite neighbouring ours) is scheduled to lose its A&E department later this year. The time it would take to get from their closed doors to the nearest alternative (by comparable private transport) is about half what it took is to get to our A&E from the relative's home, but then this closing one and its neighbours serve far denser populations, and presumably are scaled accordingly, so the loss might be on volume more be ven than time to initial triage.
Not entirely sure what precise threads of the Brexit issue this is supposed to be linked to, but it demonstrates that the stupid "£350m for the NHS!" thing was a despitically genius piece of PR, damn them, such that it seems Leave had no chance of plucking at the heartstrings so attractively, despite so easy a set of refutations.