The short answer to the question is a very long time. I know a lot of faith is being put into test and trace (t&t) and that the existing arrangements are a shambles. The system requires any person with a positive diagnosis to isolate and it seems only around 18% comply and 82% don't.
https://www.kcl.ac.uk/news/effective...on-and-support
However, any t&t system requires the population to cooperate and that isn't happening according to the independent statistics. It seems to me that t&t may not be the answer that many people believe although the government could do a lot better to communicate the need to adhere to the requirements.