We could test a random proportion daily, but the government is being devious with its numbers. It is including antibody tests and reference numbers in its capability, sending out batches unasked etc etc, and then includes NHS workers. It is likely they dont have the capacity to do a scientific random survey despite their protestations.
The ONS has a better handle on the number of deaths based on death certificates and as we know the death rate we can work back to give number of cases although there is a fiddle factor because deaths occur from day 7 to 60
At the peak we thought the total infections was 7 times the reported numbers. Now we think it is more like 4 times. So true infections in the UK probably 6000-7000 a day. A couple of papers suggest possibly 60-70% of people who are infected get NO symptoms.
Excess deaths however from Covid 19 in the mid 60,000s and when we add those who will die prematurely from delayed cancer and cardiac treatment we will be well over 100,000