The shortcut, and why it does not apply
Countries prove foreign signatures to each other in one of two ways. Inside a shared treaty, one slip does it, and every member honours the slip on sight. Outside it, the receiving state insists on looking for itself, through its own consular officer. This route is the second kind, which is why the paperwork has two stages rather than one.
Where the Central African Republic stands
The Central African Republic has not joined the Hague Apostille Convention. A British paper bound for Bangui therefore requires embassy legalisation on top of anything the Legalisation Office has already added. The United Kingdom is a party to the treaty, which is why an apostille can be issued in Britain at all, but one signatory does not make a shortcut.
The Sheffield end of the job
Nothing about the British stage happens locally, and that surprises people. There is no legalisation counter in Sheffield, or in any other city, because a single office runs the service by post. What Sheffield does supply is the source paper: the Register Office at the Town Hall for civil records, a court for a court order, an awarding body for a degree.
An apostille from United Kingdom to Central African Republic is best assembled in one go. Order the certified copies you need, send them together, and keep a spare at home. Splitting a job across several rounds doubles the post and, on a route with a small consular volume, doubles the waiting as well.
French, and the shape of a typical file
French is the working language of government there. A stamped English paper is still an English paper to the clerk reading it, so a French version usually goes with it. Prepare the words last. If the translation is made before the final consular mark, it will not describe the bundle that arrives, and that mismatch is a common cause of a return trip.
Files heading this way tend to be built around a posting rather than a move. Health, aid and research work dominate, so a police record, a degree and an employer letter often travel as one set. That is worth planning for: three papers means three British charges, three consular steps, and one calendar to keep them aligned.