A different certificate, not a smaller one
There are two ways a country can satisfy itself that a foreign signature is genuine. One is the treaty slip, honoured on sight by every state inside a shared agreement. The other is the older road, where the receiving state sends its own officer to look at the file first. Ethiopia works to the second, and the two systems do not blend into each other.
Ethiopia and the Convention
Ethiopia has not joined the Hague Apostille Convention. Britain being inside it changes nothing here, because a treaty only shortens a road when both ends have signed up to it. So there is no apostille issued in Wolverhampton for use in Ethiopia that will stand on its own, however neatly it is drawn up and however promptly it comes back.
The Wolverhampton to Ethiopia route in practice
The British half is plain and impersonal. A single national office covers the whole country, it acts through the post, and there is no counter in the West Midlands that does this work. It will mark a register copy, a court copy, or a sheet signed by someone whose hand it can trace, then send the file back the way it came.
The second half behaves nothing like the first. Where an apostille from United Kingdom to Ethiopia would have been a fixed slip at a fixed price, document legalisation for Ethiopia is handled by consular staff who read the file itself, keep their own record of it, and work to a rhythm of their own. Papers tied to a start date should leave Wolverhampton early.
Planning around the half you cannot price
One side of this road has a published number on it and the other does not, and that shapes how to plan. Treat the British fee as the fixed part of your budget and the consular stage as the open part. The same goes for the calendar: the first leg moves at postal speed, while the second belongs to a desk that answers to Ethiopia rather than to Britain.