What Edinburgh actually provides
Edinburgh Registration Service at City Chambers, 253 High Street, Edinburgh EH1 1YP, prints certified extracts of Scottish births, marriages and deaths. That extract is a signed record, not a photocopy, and every later desk works from it. It is also the only part of this route with a public counter, which is why so many people assume the rest of the job happens there too.
Where the Scottish part stops
It stops at the extract. Sudan has not joined the Hague Apostille Convention, so embassy legalisation is required, and neither stage of that chain is run from Scotland. The FCDO Legalisation Office handles British apostilles for the whole country by post from Milton Keynes, and the consular stage belongs to officials acting for Sudan. Edinburgh supplies the paper; other desks supply the marks.
What the British stage charges
Stamping costs £45 for each paper on the standard postal route, or £40 for each paper on the next-day service open to registered businesses. It is charged per paper, so sending a birth extract and a marriage extract together costs two fees but only one round of postage. An apostille from United Kingdom to Sudan is priced exactly as one bound anywhere else.
Keep the record that cannot be reissued
A birth, marriage or death record lost in transit is replaced only by beginning the request again. The way round that is a fresh certified extract from the register office named above, which carries the same standing as the paper in your drawer. Let the new extract make the journey, and the worst outcome becomes a reorder rather than a real loss.
Arabic, and the far end of the route
Arabic is the language of official life in Sudan, so an English extract commonly travels with an Arabic version beside it. That is a separate piece of work with its own cost and its own clock, and it is best begun while the British envelope is already out. The far end of this route moves at its own pace whatever Edinburgh has done.