Yes. A British citizen travelling on a full UK passport normally needs an Ordinary Visa for a Tanzania tourism trip. The United Kingdom is expressly excluded from the Commonwealth visa exemption described in Tanzania's guidelines.
The Commonwealth wording causes avoidable confusion for UK travellers. Tanzania states that many Commonwealth nationals are exempt, but specifically names the United Kingdom among the exceptions. A British passport holder should therefore not assume visa-free entry based on Commonwealth membership. For a safari, Zanzibar holiday, Kilimanjaro trek or private leisure visit, the usual route is the Ordinary Visa.
The United Kingdom is listed among nationalities able to obtain a visa online or on arrival. Tanzania Immigration recommends the online platform. Completing the process before a long-haul journey makes the status clear before check-in and creates time to correct a passport scan, photograph or date conflict without standing in an arrival queue.
Ordinary Visa guidance allows a validity of up to 90 days, but the issued grant notice and border endorsement control the actual stay. Tourism permission does not cover Tanzanian employment or an activity requiring a Business, Student or other visa. The category must reflect what the traveller will genuinely do.