More than 40,000 people have installed the smartphone software so far.
The health service is targeting the Isle of Wight only, at this stage, but it says this is the first stage of the app's rollout – not a test.
Tests carried out on behalf of BBC News confirm the developers have found a way to work round restrictions Apple places on the use of Bluetooth in iPhones.
In a related development, Health Secretary Matt Hancock has announced that Baroness Dido Harding will head up the wider test, track and trace programme.
The appointment has surprised some given that when she was chief executive of TalkTalk, the internet provider suffered a major data breach and failed to properly notify affected customers.
The NHS Covid-19 app is designed to use people's smartphones to keep track of when they come close to each other and for how long, by sending wireless Bluetooth signals.