Apostille vs. Embassy legalisation for Tanzania
The first instinct on being told an apostille will not do is to look harder at the document. People order a newer copy, ask for an extra signature, or pay for a stamp they hope will carry more weight. None of it helps here, because the certificate was never being judged in the first place and no amount of polish changes where it can be used.
What is actually being judged is a relationship between governments. An apostille issued in Wolverhampton for use in Tanzania would be perfectly valid as a British act, and simply lands in a country that never agreed to treat it as sufficient. Once you see the obstacle in the right place, the next step becomes obvious rather than frustrating.
Tanzania's Hague status and what it means
Tanzania has not joined the Hague Apostille Convention. That is a statement about a country, made once, and it applies equally to a school transcript, a company filing and a marriage entry from the same family. It is also the only piece of information you need in order to choose the route, which is why the choice takes seconds rather than research.
The Wolverhampton to Tanzania route step by step
Start with a sealed British paper, which is the shared foundation of both routes. Births, marriages and deaths held locally can be reissued as certified copies by Wolverhampton Register Office, Civic Centre, St Peter's Square, Wolverhampton WV1 1RU. Other documents are sealed by whichever body produced them, so a degree, a court order and a company record each begin somewhere different.
From there the paper goes through consular legalisation rather than to a single certifying desk. Because the receiving state checks for itself, the sheet passes through more hands than it would on a treaty corridor. Send a certified copy and keep your own original at home, and do not break any seal or fastening an office has already applied.
Cost and timing for this route
No fixed published figure covers a consular route, and a price you find quoted for some other country describes that country alone. An official fee applies at each stage the paper passes, so the number of stages sets the total. Allow noticeably more calendar time than a single stamp would take, since several offices are involved in turn.
What this means for the rest of your paperwork
If you are sending papers to more than one country, sort them by destination before you do anything else. The same certified copy that finishes in one envelope may need the longer route in the next, and the difference has nothing to do with which document is more important. Sorting by destination first saves you from paying twice for the same sheet.