The Joint Committee on Vaccination and Immunisation (JCVI) has advised the government to prioritise people for the coronavirus vaccine who are over 16 and living with severely immunosuppressed adults, such as those on immunosuppressive treatment.
They do not currently advise vaccination of household contacts of immunosuppressed children, or household contacts of immunosuppressed adults who are themselves children.
You can read more about this update and why this decision has been made on the government’s news page here.