We can get an idea of cases via hospital admissions. We don't need to know the exact number.
However, in the first wave, there was a far higher threshold for hospital admission with covid.
So it's not a straightforward measure.
Even with deaths, there are arguments about whether to include the many people who died from covid more than 28 days after they tested positive. And the arguments about how many people testing positive from covid should have this on their death certificate.
it's hard to see why there should be a problem just providing information (about case numbers, admissions and deaths) which is of public interest that is easily available.
Meanwhile, there is always the ONS survey. And sewage of course 