Another issue with bluetooth is the sheer distance at which it works.
For example i can lay my phone on the floor in the front corner of the gym, and it will still pick up my wireless headphones if i am out the back in the toilet/changing/boxing areas.
At home, i can leave my phone on a chair in the back garden and go and do a treadmill session in the front garage with no issues...
Last week we had Severn Trent in the street fixing a leak/crack. They were certainly within Bluetooth range for about 5 hours, without me ever being within about 15 metres of them (indeed i didn't even leave the house that day)
But if one of them tested/diagnosed as positive, would using the app then mean i am expected to isolate...
From an outside (and decidedly non-expert) viewpoint, the whole scheme seems riddled with potential errors. I'll refrain from posting anything contentious about the NHS and my thoughts on their chances of actually producing a working App...