This is the privacy notice I got.
contact-tracing.phe.gov.uk/help/privacy-notice
If you have been told by NHS Test and Trace to self-isolate
If you test positive for coronavirus or are a close contact of someone who tests positive, you must self-isolate to stop the virus from spreading. If you have been instructed to self-isolate by NHS Test and Trace, we will regularly contact you by phone and text during this period to provide advice and support and check you are self-isolating.
If we try to call you but receive no response after three attempts or if you tell us you are not self-isolating, your name, address at which you are self-isolating, contact details and information about when you were instructed to self-isolate will be provided to your local authority. Your local authority will investigate further to find out if you need support with self-isolating or have a reasonable excuse not to self-isolate. Reasonable excuses include seeking medical assistance, obtaining basic necessities such as food or medicine if there is no other way to obtain them, accessing social services or other important public services, avoiding a risk of harm, attending the funeral of a close family member, carrying out a legal obligation such as attending court, or accessing veterinary services. If there is evidence to suggest you are not complying with the duty to self-isolate without reasonable justification, your local authority may pass this information on to local Police to investigate further. This may lead to enforcement action being taken against you, which could include you being fined.
If the Police receive a report that you may be breaking the self-isolation requirement, they may ask us to confirm if you were required to self-isolate and for what time period. We will share with the Police information including your name, the address at which you are self-isolating, details about your self-isolation, and other information they may need to help decide whether to take enforcement action against you.
If you test positive for coronavirus
If you test positive for coronavirus you will be contacted by the contact-tracing service and asked to confirm or provide your:
full name
date of birth
sex
ethnic group
NHS number
home postcode and house number
mobile phone number
telephone number
email address
You will also be asked to provide:
details of your COVID-19 symptoms, including when they started and their nature
whether you are clinically vulnerable or extremely vulnerable and require support
details of people who are your close contacts and how you came into contact with them