From 28th November, all vaccinated travellers arriving into the UK should quarantine at home and take a Day 2 PCR test. You can leave isolation when your negative result is confirmed. This change is due to a new variant of concern originating in Southern Africa.
The rules for unvaccinated travellers remain unchanged: if you are arriving into the UK and your are not fully vaccinated you are required to take a pre-departure Lateral Flow Test before setting off for the UK, and then self-isolate for 10 Days upon arrival, taking a Day 2 and 8 PCR Test during that time. You must book these test before coming into the UK. If you're unvaccinated and taking both Day 2 and 8 Tests, you have the option to take an additional test on Day 5 of your quarantine, called a Test to Release.