Test and trace is the centre-piece of the USA's exit from lockdown, South Korea etc. It will choke off the virus and is doing in those countries which are executing it, however, I think the UK is reluctant to do it too soon. I think they would like to keep the infection rate relatively high so that immunity is acquired but at the same time they want to prevent the hospitals from being overwhelmed. Once we've got a significant amount on infection in society I think they want to keep the infection ticking a long at a steady rate. That way we are closer to acquiring immunity. I don't agree with this approach but I think it is what they are up to because it explains everything we see them doing, or not doing.
Did you see that the Swedish epidemiologist is claiming that Stockholm maybe close to acquiring immunity? I don't believe that. They have still been social distancing but just not as strongly as other countries.