Why the search comes up empty
You cannot legalize documents for Nicaragua at a mission counter, because the destination does not ask for that stage. It accepts a single-step certification done in Britain. That is why every hour spent looking for a consular desk turns up nothing: the desk is not hiding, it is simply not part of this route.
What a finished file looks like
A completed job here is thinner than people expect. One certified paper, one British mark, and no further layer. Embassy attestation for Nicaragua would be an extra sheet on top of that, and it is not produced for this destination, so its absence is not a gap in your file.
Recognising the finished state matters practically. It is what lets you post the file onward, book the appointment or close the matter. Waiting for consular legalization for Nicaragua that nobody issues is how a job that took ten days ends up taking six weeks with nothing to show for the extra time.
Starting the job in Southampton
The work you can actually do sits at the beginning. Southampton Register Office at 6a Bugle Street, Southampton SO14 2AJ supplies fresh certified copies of birth, marriage and death entries, so the record you keep at home never has to make the journey. For other kinds of paper the certified version comes from whoever issued or holds it.
After that the file goes to the FCDO Legalisation Office and comes back. Someone handling embassy legalization for Nicaragua from Southampton is therefore managing two things only: getting the right certified paper, and one turnaround. There is no third moving part to coordinate.
Cost and calendar
An official fee applies for the British certification. It is charged per paper, so the total is set by how many separate records you are putting through rather than by the destination. Standard handling takes 7–10 business days and the faster option takes 2–3 business days.
Both of those are firm enough to plan around, which is not always true elsewhere. Because document legalization for Nicaragua involves one office and one queue, the range you are given at the start is the range you get, and a deadline two weeks out is comfortably safe.
One habit worth keeping
Write down, at the outset, what the finished file is meant to be. A single line — one certified paper, one British mark — is enough. It stops the job drifting when a well-meaning colleague suggests a stamp that does not exist, and it gives you a clear point at which the work is over and the paper can be sent.