Why the apostille is not the stamp you need
An apostille is a single slip one country attaches so another will read a paper without further checks. It only works when both ends have signed the same treaty. Central African Republic has not joined the Hague Apostille Convention, so that shortcut is closed and a longer chain takes its place. An apostille from United Kingdom to Central African Republic ends the British half of the job without finishing the whole of it.
What the consular stage actually does
Consular legalisation means an official acting for the receiving country looks at the British paperwork and adds a mark of their own. That mark is what a desk in Bangui will recognise. It is a different act from the British stamp, done by different people, and it carries its own fee and its own queue. Treating the two as one step is where most timetables go wrong.
What Edinburgh can and cannot do
Edinburgh's part is the beginning, not the end. Edinburgh Registration Service at City Chambers, 253 High Street, Edinburgh EH1 1YP, prints certified extracts of Scottish births, marriages and deaths, and those extracts are what the rest of the chain works on. The stamping itself happens elsewhere: the FCDO Legalisation Office runs by post from Milton Keynes and keeps no counter, so nobody gains by travelling to it.
Pricing a route with an open end
The British charge is fixed and easy to plan around: £45 for each paper by post, or £40 for each paper on the next-day route open to registered firms. Everything after that is less tidy. The consular stage sets its own fee and its own pace, and a file can sit there while nothing visible happens. Build your slack in at that end rather than the British one.
Language, condition and a long journey
Two things decide whether a file is usable when it lands. The first is language, because French runs official life there and an English extract usually travels with a French one. The second is condition. A page that arrives creased, torn or with a slip pulled loose invites questions nobody can settle from a distance, so pack it flat and scan every sheet before it leaves you.