There may be an incredibly small number who had other critical illness in addition to their Covid-19 diagnosis
Average lifespan in a senior citizens home is about 5 years. So when the virus rages through one of the homes, the majority are close to death anyway. They might have survived a year or two longer. But then many of the elderly die of pneumonia caused by influenza in normal years - hence the saying "pneumonia the old man's friend".
For comparison of the 500,000 who die each year in the UK, around 125000 people die of cancer, and a similar number from heart disease. Neither of those are particularly pleasant deaths - especially cancer.
Considering the impact of flu - in 2012 28,952 people died of pneumonia, more than likely viral pneumonia from influenza. Of those 27,520 were over 65. In 2015 as you suggest excess deaths suggest 28000 died from influenza.
As Alvez said what we need more than anything is to know how many people are infected. And for that we need antibody tests. If we know that 30% of the population have been infected (or even more as per the U of Oxford analysis) then the government can select the right strategy. We'll have a far better idea about the pressure on the NHS - which is really what the lock down is all about. They need to get some kind of test out into the field instead of farting about. Even a test that had errors could be useful for statistical analysis. As long as you know the error rate.
Icelandic research suggests 50% of all those tested were asymptomatic. And in numbers per million they've still tested more than anyone else. (Their mortality rate is currently 0.3% - not even as bad as a bad flu year - but it could get worse over time). Since the virus can survive on fomites for some time, it's likely even in Iceland a certain percentage had the virus without manifesting symptoms and were never tested. So the virus may be considerably more widespread than the figures suggest.
It isn't complex math to take the current assumed infection rate (2.6 per infected person) with a 5 day incubation (on average) and project the progress of this disease. About now without mitigation it takes off like a rocket and would infect half the country by late April. It all depends on when the virus first reached the country. If it was mid January, then many people might have had the virus without knowing, and doctors might not have realised they were treating Covid-19 because until mid January China didn't let on it was infectious. Even in late January the WHO were still saying not to worry about it.