There was a news item yesterday about the topic of testing centres being empty. There are multiple centres but only a handful of mega-labs that can process the tests, so the bottleneck is the capacity to process the tests, rather than take the samples in the first place.
As an aside, I went for an antibody test through my work as a doctor. Took two weeks to book, and three weeks after my blood was taken, I hadn't had a result. Phoned to chase it and was told the sample had been lost. Working in the NHS for a number of years meant I wasn't surprised by this ineptitude, and even less so two weeks later when I got an email with the result. Total time from booking to result was 7 weeks. I'm not sure as a healthcare professional what I could meaningfully do with that information after such time had lapsed.
The above is just an anecdote, but the NHS has been operating on such a knife-edge for so long that parts of it are simply basket cases. I just wish people would wake up to this, stop the sentimental fetishising of the NHS that makes us all feel warm and cosy, and think about the hard realities of how we want to fund a universal healthcare system and social care for an increasingly elderly population with multiple co-morbidities. There are no easy answers but burying our heads isn't an option either.