A little data on excess deaths v covid deaths in Greater Manchester:
https://medium.com/@urbixio/greater-manchester-covid-19-related-excess-deaths-c382c95b14f
On the face of it, it looks like a lot of the reporting coming in from (non-hospital) death certificates comes down to what local GPs and coroners are taking as policy, and a stance on "most likely" cause, or even on documenting deaths amongst people with other illnesses.
In Bolton for example, "Bolton reported 472 deaths in April 2020 and have had a yearly average of 222 for the month. There have been 168 Covid-19 deaths reported which would be a difference of 82 deaths above the yearly average and Covid-19 toll."
Whereas in its neighbouring town, Bury: "Bury reported 282 deaths in April 2020 and have had a yearly average of 155 for the month. There have been 110 Covid-19 deaths reported which would be a difference of 17 deaths above the yearly average and Covid-19 toll."
Some of these may be timing related. Others may come down to an individual outbreak (in a care home or something) that isn't described wholly by the numbers. But still, it sounds like the recording may come down to policies adopted by individual GPs/GP practices. Certainly that Bury number seems more credible than the Bolton one. It would be interesting to know if that kind of policy divergence is taking place in other health authorities as well.