SAGE is using a figure of 1% false positive results. I think it is a little lower ~0.8% for Pillar 2. False positives are a function of the population tested as well as imperfect testing. (Nothing is perfect).
https://www.hdruk.ac.uk/projects/false-positives/
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https://www.hdruk.ac.uk/projects/false-positives/
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Government published guidance on Mon 7th to attempt to address the problem of false positive results. 2/24 https://www.gov.uk/government/publications/sars-cov-2-rna-testing-assurance-of-positive-results-during-periods-of-low-prevalence/assurance-of-sars-cov-2-rna-positive-results-during-periods-of-low-prevalence
The jury is out on how big a problem this is but, having analysed the data I think it accounts for almost all results through the summer 3/24 https://lockdownsceptics.org/when-is-covid-19-not-covid-19/
Since the end of June we have seen positive tests account for 1% or fewer of the tests performed. The increased numbers of tests makes for more positive tests but the percentage is still negligible. 4/24 https://twitter.com/TechClive/status/1303332369580142592?s=20
This has allowed us to establish what the false positive rate is for the different populations being tested. Community testing having a higher proportion of symptomatic patients, results in a higher false positive. 5/24 https://logicinthetimeofcovid.com/2020/09/08/variation-in-the-false-positive-rate-2/