I thought it wasn't going to track your location at all. It was going to exchange a code with other phones that were in close enough proximity for a certain amount of time, and then if someone registered that they had symptoms, a message could be sent to all those phones that had the code of the ill person's.
I don't know how well it would work in terms of contaminated surfaces - eg., if you were on a tube carriage directly after someone who had it, you wouldn't get any messages, but might be at a fair bit of risk.
People would also need to be able to get tested even with minor symptoms (or eventually, even if asymptomatic), and it doesn't sound like there will be the capacity for that for ages.