My suspicion for months was that they would 'repurpose' the NHS contact tracing app to do just this. Eg. see
this post from September.
I will be very happy indeed if my suspicions aren't realised!
You would suspect if this was planned then they'd have been ready to roll it out when the vaccinations started. So the fact they didn't is a positive sign.
They have been all over the place, on this as much else. Though even when they are clear, they change their mind a few days later, so I'm not sure it would help much.