A mark comes from the country that issued the paper
A stamp of this kind always comes from the country that issued the paper, never from the country that will read it. A British birth record, a British court order or a British company filing is a British errand from beginning to end. No office abroad can speak for a signature written here, which is why nothing on this route is arranged at the far end.
Both offices are on this side
Tanzania has not joined the Hague Apostille Convention, so document legalisation for Tanzania takes a second stamp above the British one. The useful part is that the second stamp is also collected here, from the consular staff who act for that country in Britain. Two offices, one country, and a single finished bundle at the end of it.
That changes how the job feels to run. An apostille from United Kingdom to Tanzania is not a request you send abroad and then wait on; it is a short chain of local errands you work through yourself, in order, with a known charge at the first of them. The waiting starts only once the completed file has gone.
What that means for planning
Because everything is local, the only thing you genuinely need from abroad is the list of papers wanted. Work from that list and the route stays under your own hand: order the sheets, get the first stamp, get the second, send once. A file that leaves the country half-finished is the one that generates a return journey nobody budgeted for.
Westminster Register Office at 317 Harrow Road, London W9 3RJ issues fresh certified copies of birth, marriage and death records, so no personal certificate has to cross a border. The Legalisation Office charges £45 per document by post, or £40 per document on its next-day line for a registered business, and it works entirely through the post.
Send it whole, and send it once
So what you need for an apostille for Tanzania is a signed British version of each paper, the British charge for each one, and the consular stamp in place before anything is posted abroad. A finished file arriving in one piece is worth far more than a quick file arriving in two.