It's worth highlighting the differences between the UK and the rest of the world. The NHS is embedded into the UK's culture. Since the start of lockdown, drawings of rainbows are commonly seen in windows with captions like 'Thank you NHS and key workers' and on Thursdays at 8pm, people stand on doorsteps and clap for the NHS. The NHS is very well trusted and this app, if viewed as a creation of NHS (or NHSX) and not 'the government', could still remain successful despite privacy concerns.

Unlike other countries, the UK has the opportunity to frame this as an NHS-created app, rather than a state-created app. If they're able to do that, then it wouldn't surprise me that the UK's population takes up the app.

Additionally, few people consider data privacy concerns at the best of times. Given the circumstances, I think more people are willing to prioritise public health over privacy concerns.[1] So, they seem to have judged that the richer data trumps the slight reduction in usage.

The combination of these factors could be the rationale behind this judgment call.

[1] https://www.ft.com/content/1752affb-24dc-4ad9-8503-78f9ce1ad... (there's a paywall, so the link below shows a similar poll)

[2] Ipsos MORI poll https://www.ipsos.com/sites/default/files/2020-04/coronaviru...