Why it won't work
As others have pointed out, it's not going to work. Take the example of going to work in London after lockdown is eased. Bluetooth just loves propagating in metal boxes like the tube, escalators and buses, so you can expect 50 - 100 contacts to be logged on your trips in and out of work each day. If you've just caught Covid, you'll do that daily trip five times during the infectious, presymptomatic stage, which means 500 or more people will have you logged on their phone. On day six, when you self-isolate and get yourself tested, they’ll all get a message telling them to self-isolate and get a test.
With a working population of 6 million in London, we’ll see more than one new infection each day. If the infection rate is 0.01%, which is optimistically low, then that’s 600 infected people going to work, meaning 300,000 people with the tracing app will be told to self-isolate on day 6, or whenever the test results come through.
This is very Noddy maths. There will be quite a number of repeat contacts, as most people do the same journey each day, but that will be balanced by the new infections that join the spreading team on days 2,3,4,5, etc. However, it’s a good enough finger in the air check to alert you to the fact that we would need around a quarter of a million home-administered tests EVERY DAY. Otherwise, those 300,000 people sent home will be sitting around at home for three or four days to get their test results. Only a few hundred are likely to be infected, but if it takes four days for them to be cleared, the app will have locked down a quarter of London’s workforce.
It gets worse. Once they have the all clear and get back to work, it’s probably only going to be a few days before one of their new contacts is tested positive and they’re sent home again. After a couple of cycles of that, I can’t see users continuing to use the app.
Tracing and isolating is really important, but it starts with having massive home-testing available. A tracing app will make that much more effective, but you need the organ-grinder first, not the monkey, however much our politicians may identify with the latter.