The government said people with no document can have access to vaccine of Covid-19 with no repercussion, as long as they are registered with a local surgery.
It is important to mention that people can register with a surgery without documents (but an address is required for correspondence).The individual can give a phone number and the surgery address if they chose to do so. It is called primary healthcare, but for the secondary healthcare doctors are require to check the individual immigration status as charges could be applied.
https://www.bbc.com/news/uk-politics-55978334