Where one authority stops
An apostille issued in Brighton for use in Sierra Leone is not accepted, and the reason is worth stating plainly rather than treating as a quirk. Every official mark carries the authority of the body that made it, and no further. A British certificate is a British statement about a British paper. Whether another state acts on it is that state's decision, made under its own rules.
Where two countries have agreed in advance to recognise one another's certificates, the chain can be short, because the agreement does the work that a second desk would otherwise have to do. Without such an arrangement between them, nothing is missing from the British certificate itself. It simply stops at the edge of what it was ever entitled to say.
What each side is entitled to say
The British half has a narrow and honest job. Brighton & Hove Register Office speaks for the register it keeps and issues certified copies of births, marriages and deaths recorded in this district. The Legalisation Office (Foreign, Commonwealth & Development Office) then certifies British public papers for use abroad, and each body confines itself to what it actually holds.
The other half belongs to a consular authority answering to Sierra Leone, and it decides on that state's behalf. Nothing in the British chain instructs it, and nothing it does reaches backwards to change what the British marks mean. The two halves sit end to end rather than overlapping, which is why the order they run in is not negotiable.
What the boundary rules out
It rules out shortcuts that sound reasonable. A British desk cannot waive the later stage, cannot confirm in advance how the far end will treat your paper, and cannot make its own certificate travel further by adding something to it. An apostille from United Kingdom to Sierra Leone is not a stronger version of the same thing; it is simply the certificate the other agreement would have used.
It also rules out a common misreading of delay. When a file stalls after the British stage, the British stage is rarely the cause, because its part is already finished and its record of that is on the sheet. Looking for the hold-up on the side that currently holds the paper is a faster habit than re-examining work that is already complete.
Working sensibly with a handoff
Treat the route as two jobs with a fixed join rather than one long queue. Finish the first cleanly: the right sheet, the right number of copies, the correct official certification on each. Then present a complete first half at the boundary, because an incomplete one does not get partially accepted there — it comes back for the missing piece and the clock restarts.
Keep your own record of what the first half produced, with dates. Knowing what you need for an apostille for Sierra Leone matters less than being able to show, later, exactly what was certified and when. The second authority sees only what arrives in front of it, so the history of the file exists nowhere except in the paper and in your notes.