The daily death rate that is announced to the public is people who have died in hospital who have tested positive for the virus.
The ONS is including anyone who showed symptoms.
**** knows why they can't agree on a system, although I could hazard a guess.
https://www.bbc.com/future/article/20200401-coronavirus-why-death-and-mortality-rates-differ
"In the UK, for example, the Department of Health and Social Care releases daily updates on how many people who tested positive for Covid-19 died that day. This includes any patient who tested positive for Covid-19 but who might have died from another condition (for example, terminal cancer). But the UK’s Office for National Statistics counts all deaths as Covid-19 where Covid-19 was mentioned on the death certificate, regardless of whether they were tested or if it was merely a suspected case of Covid-19. Adding to the complexity of trying to understand the death rates is that the two are out of sync, since the ONS way of counting can only happen after a death certificate has been issued, so takes longer."