You don't need to self-isolate if you are double vaccinated and get pinged by the app. You are advised to take a PCR test but there is no compulsion.
From 16 August 2021, if you come into close contact of someone with
COVID-19, you will no longer need to self-isolate if you are ... fully
vaccinated and it has been two weeks since your final dose of an
MHRA-approved vaccine in the UK vaccination programme.
You don't need to self-isolate if you are double vaccinated and get pinged by the app. You are advised to take a PCR test but there is no compulsion.
https://faq.covid19.nhs.uk/article/KA-01380/en-us