I still think the main failing in the way this is being handled in the UK (and the US for that matter) is the lack of widespread testing. As the head of the WHO head pointed out, the key to tackling this virus is: test, test, test. If you don't know who's got the virus, how many cases there are and where they're located, you're working blind.
One of the worst aspects of the failure to test in the UK is the refusal to screen health care workers even when they've been exposed to patients with coronavirus or have symptoms but only mild ones. This means you're letting possibly infected health care workers continue to treat some of the most vulnerable people in society (remember that according to some studies in China, up to 86% of cases may be asymptomatic). An NHS doctor talks about the failure to test in the article below:
NHS staff and CoVid-19 tests.
In China, they were able to get this under control because they tested every single person who showed even the slightest symptoms in special fever testing facilities, isolated from other hospital areas. After ruling out other causes like flu or bacterial pneumonia, they would test for the coronavirus and get the results back within four hours. See video below explaining how this worked.
I mentioned this before but if you don't do sufficient testing, and just isolate people without knowing whether they're actually infected or not, you're spending time and effort on possibly unnecessary measures while allowing other, potentially infected people to keep on spreading it.
Asking people to self-isolate at home can also be counter-productive as even when you're trying to be careful it can still get passed on to other family members - as the video about virus testing in China also mentions, 75-80% of cases there turned out to be from family members infecting each other. Having learned that, they started isolating people who were positive in separate facilities to avoid family transmission.