Here are the rules, Gov website. In summary double jabbers don’t need to isolate if identified by contact tracing but do if they test positive themselves.
‘From Monday 16 August, people who are double jabbed or aged under 18 will no longer be legally required to self-isolate if they are...
You can be pinged with any number of days to isolate. For example I was pinged after a flight and told to isolate for 5 days. It won’t be 10 days from a close contact but impossible to predict if just how many.