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lynx
@Greenbank
ONS are testing ~140,000 households monthly.
Assuming that's a 7 day operation (no reason to think otherwise, we've had our tests done on all different days, including Sundays) that's ~4500 households per day. And the results are generally within 3-5 days (only rarely will they be faster than that).
Assuming an average of just over 2 people per household to give 10,000 people tested per day that means you're testing 1 in ~6700 people per day in the country, irrespective of whether they think they have an infection or not, with a 3-5 day turnaround. That's going to give you a pretty good clue about prevalence as long as the households provide suitable coverage over the UK (which I'm sure they are).
Of course, there might be some bias in the type of people that will make themselves available for a monthly ONS test. I'm sure they're able to understand this and factor it in though.