This is an article by Daniel Curtis.
The following chart was built with data from a csv file downloaded from Our World in Data (downloaded on 11 Aug 2020 at 08:49). The vertical axis (logged, for clarity) shows the daily test positive rate for the UK, where ‘test positive rate’ is defined as the percentage of new_tests showing new_cases, as derived from their respective columns in the csv file (i.e. 100 x new_cases/new_tests). The horizontal axis shows the date.
The test positives will be the sum of both true and false positives. If the ratio of false positives to number of tests is assumed to be constant then the overall test positive rate will level off at a constant minimum when the ratio of true positives to number of tests reaches its baseline. This will be when true positives either (a) reach zero, or (b) persist at a small yet stubborn constant rate. The results from any further testing might be expected to be randomly distributed around this point.
From the chart it appears that the test positive rate levelled off in such a way from 30 June. The rate from that point to the latest date (30 Jun to 8 Aug) – excluding an apparent outlier (0.05% on 29 Jul) – has a mean of 0.553% and SD of 0.096%. The distribution of residuals around this mean is not significantly different from normal (Kolmogorov-Smirnov test statistic (D) = 0.168, p = 0.198).
On this basis, the data suggest the prevalence of Covid in the UK reached a minimum on 30 June and has remained constant since.
Existing surveillance measures report on absolute numbers of test positives. Given that prevalence has been shown to be constant since 30 June, these numbers will have varied only as a function of daily number of tests taken. They will not have indicated any change in prevalence. Future monitoring should look for diversion from the baseline test positive rate rather than absolute numbers of test positives.