Seems a bit click baity to me. The app doesn't claim to be super accurate, and if someone has their diagnosis confirmed it can at least show if they've been self isolating, or been in relative close proximity with lots of people. And of course, it can't know if someone has been in contact with someone without a phone.
It isn't meant to completely track everyone, the question is - is it better than nothing?
No-one is claiming an app can magically know everyone who will get it, but it should at least help modify peoples behavior by informing them if they've been near a confirmed case. They'll probably have to tweak it to reduce the false positives, and there will be plenty of false negatives but some feedback is better than none.
Bluetooth low energy has enough range to be received much further away than what is a safe distance for COVID-19. Especially if there are metal objects nearby which may act as RF reflectors or blockers.
For example, lets assume that 40 people are riding on a bus and that 35 of them have cell phones with BTLE turned on. The interior of the bus, desite the existence of windows, will be likely to concentrate the RF so that all the phones receive more signals from one another even if they are on opposite ends of the bus.
So, as far as proximity, even if only four people are near enough to somebody with covid-19 to possibly have picked up the virus, it would be likely that far more than four people might show as having been close, even people far away. Most of us have been in a large round room, or one with a curved roof. A so called whispering gallery, You can stand on one side of the round room and somebody else can stand at its exact opposite nodal point and hear you whisper. Effects like that are common with RF.
An RTLSDR can be useful in showing how much UHF signals vary as you move an antenna around.
I don't see how any of that really matters. Over the last 7 weeks we've had blanket social distancing: assuming everyone is infected and physically isolating everyone from one another, as much as possible to prevent transmission. This was a very blunt tool which cut R below 1, at huge economic cost. What the government should have done right from the beginning, was more testing and contact tracing and testing, as has been the case in Taiwan and South Korea, which haven't had so much social distancing. Now the infection rate has been reduced to manageable levels, the idea is we can sharpen our a approach and work towards only isolating those who are most likely to have the virus. Ideally we should be able to test everyone who's most likely to have the virus, then they can be free to return to work.
The app is just another tool to help with contact tracing. Now we only need to isolate everyone on the bus, rather than the whole country and because it's a relatively small number of people, it's more feasible to test everyone one of them and the friends and family of those who test positive. In the UK, the app will be voluntary and I believe it will still have a positive effect, even if not everyone uses it. If it's proven to be effective enough, then there should be some incentives for people to use it such as being able to jump long queues to enter supermarkets more quickly and perhaps money off certain items such as toilet paper.

Other measures which many may consider to be big-brotherish will be required. For example, if a nightclub is opened, everyone going will need to show photo-ID on the door, then if anyone feels unwell afterwards and test positive, everyone who visited the club on that night, along with anyone they've been in close contact with, will have to be tested and self-isolate if appropriate. A similar thing will need to be done in other situations where social distancing is impossible, such as crowded public transport. The app should only be a small part of the programme of testing and treatment/isolation of the infected.
If governments invest hugely in contact tracing and targeted testing, we can all get back to work and play fairly quickly and the tax revenues will easily pay for it.
To those who are concerned about big brother: they have a right to be, but don't forget many of these measures will be costly and governments won't want to spend money on them when they're no longer needed. I can't even see China bothering to waste money on recording the name and address of everyone entering a crowded bar.