The government guidance is clear
https://www.gov.uk/government/publications/covid-19-stay-at-home-guidance/stay-at-home-guidance-for-households-with-possible-coronavirus-covid-19-infection#will-my-household-be-tested-if-we-think-we-have-covid-19-symptoms
Why staying at home is very important
It is very important that people with symptoms of or a positive COVID-19 test and their household members stay at home. Staying at home will help prevent the spread of the virus to family, friends, the wider community, and particularly those who are clinically extremely vulnerable.
If you have symptoms of COVID-19 or a positive test, remain at home for at least 10 days after the onset of your symptoms (see ending self-isolation below). This will reduce the risk of you infecting others.
If you have symptoms of COVID-19 or a positive test, then you should avoid contact with other household members as much as possible.
Other members of your household, including those who do not have any symptoms, need to stay at home and not leave the house for 14 days. Do not go out even to buy food or other essentials, and any exercise should be taken within your home. This 14-day period starts from the day when the first person in your house became ill or if they do not have symptoms, from the day their test was taken. There is more information in the ending self-isolation section below.
https://www.nhs.uk/conditions/coronavirus-covid-19/self-isolation-and-treatment/when-to-self-isolate-and-what-to-do/
When to self-isolate
You must self-isolate immediately if:
you have any symptoms of coronavirus (a high temperature, a new, continuous cough or a loss or change to your sense of smell or taste)
you've tested positive for coronavirus – this means you have coronavirus
you live with someone who has symptoms or tested positive
someone in your support bubble has symptoms or tested positive
you're told to self-isolate by NHS Test and Trace
you arrive in the UK from a country with a high coronavirus risk – see GOV.UK: how to self-isolate when you travel to the UK
