You do not need to quarantine or take a day 8 test after you arrive in England if you are either:
Fully vaccinated in the UK or under the UK vaccine programme overseas
Under 18 on the day you arrive in England and resident in the UK or in a country with a vaccination programme approved by the UK
Part of a UK-approved vaccine trial
You must have had your final dose of the vaccine at least 14 whole days before the date you arrive in England. You still need to book and take a day 2 test