Government and official
DVLA (licence AND logbook — they're separate updates), HMRC, the electoral roll (register at the new address), council tax (close the old account, open the new one — you may be owed a refund), and TV Licensing. If you receive any benefits or pension, update DWP too.
Money
Banks and building societies, credit cards, loan providers, pension schemes, and every insurer — car insurance is legally invalid at a wrong address, so do that one before the van moves. Update premium bonds and any investment platforms while you're at it.
Home and utilities
Energy suppliers (final meter readings, photographed), water, broadband (book the new installation weeks ahead), and Royal Mail redirection — the safety net that catches everyone you forgot. Three months minimum; twelve is safer.
Health, work and the forgotten ones
GP, dentist, optician, vet — and schools, which have their own timelines for transfers. Then the forgotten tier: subscriptions and deliveries, loyalty schemes, the gym (check the contract), online retailers with saved addresses, and your breakdown cover.
Finally, tell people: neighbours who might take parcels, and whoever holds your spare key.