Why people go looking for a place
It is natural to look for somewhere to go. Legalisation feels like the sort of business that ought to have a counter, a queue and a clerk who stamps things while you wait. On this road no such place exists, and hunting for one costs days that no later stage will give back to you.
Where Gabon stands
Gabon has not joined the Hague Apostille Convention. Documents intended for Gabon need embassy legalisation instead, so the desk that decides the matter sits abroad and no British stage can close the file. That is a fact about the country at the far end, and it would read the same for a sender in any other British city.
The one local address
Leeds Register Office at 2 Great George Street, Leeds LS2 8BA is the single address here that changes anything. It holds the births, marriages and deaths registered in the city and issues certified copies from those entries. A copy ordered from it is a fresh official issue, so the certificate you keep never has to leave your drawer.
An office that is a post box
The British apostille authority is, in practice, a post box: PO Box 6255, Milton Keynes MK10 1XX. It issues every apostille in the country and it works by post, with nothing to attend in person. Anyone reading up on what you need for an apostille for Gabon finds that address early and then finds it belongs to a different route.