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I imagine that public transport is the main issue there. London isn't really going to get back on its feet until public transport is working at a decent capacity and, by its nature, public transport is somewhere where you spend extended periods of time in close confinement with strangers.
For other areas of the country, mainly outside of the cities, where public transport usage is much lower it's probably less of an issue.
Depends how much anonymous contact you think you have where the app would give something above the contact tracing call centre.
Most places do fine without an app.