Since the reporting on death stats is so fucking terrible, here's my attempt to set down my understanding. Apologies in advance if bits of it are patronising as fuck to some people.
Hospitals record deaths of people who have
recently[1] tested positive for COVID-19. These appear in the
daily reported deaths figures, but there's often a lag of a few days. (See
English figures by day-of-death here..)
The ONS publish
weekly deaths based on death certificates - this shows you all deaths, deaths involving an underlying cause of a respiratory disease or condition
[2] and now deaths with any mention of COVID-19
[3]. "Any mention" here means pretty much you just have to write "COVID-19" somewhere on the death certificate - not that COVID-19 is what, fundamentally, killed this person. These deaths include deaths anywhere, not just in hospital.
Note that death certificates are frequently filled out by the least experienced and qualified medics available, and that they've often had very little contact with the deceased before they died. A lot of the fallout from Shipman was that death certification was a bit rubbish, and that we needed to setup a proper system for reviewing deaths (which we're finally doing after UK Government decided to pay for it).
A fair number of people who died from COVID-19 out of hospital will not have "COVID-19" written on their death certificate anywhere. In many cases, doctors might feel that they suspect COVID-19 was involved, but given that they don't have a positive test might not feel it's appropriate to write it on the certificate. They will probably have "pneumonia" on there somewhere. At the same time, a fair number of people whose deaths involve pneumonia, or COPD etc.,
won't have COVID-19.
Death registration also has a considerable lag, and this is possibly particularly bad at the moment because of discouraging travelling.
I don't think that not including care home deaths is a ruse by any of the four governments of the UK. I think it reflects that it's hard to get rapid and reliable reporting of community deaths, even in communal establishments. Focusing on hospitals and positive-tests at least gives a
consistently biased picture of the situation with only a few days lag.
[4]Right now, relatively few people with COVID-19 on their death certificates are dying in care homes
[5] - of course, some of that is biased testing (including perhaps because it's not
useful to keep testing symptomatic residents in a care home that you know that there is an outbreak in
[6]).
The ONS provide enough data that I think it's hard to cover up under-reporting at a national level; ultimately we can see total excess deaths with only about a fortnight's delay.
