Membership belongs to the receiver, not the sender
A treaty is a promise between countries to accept each other's slips without further checking. Britain made that promise long ago, which is why the certificate exists here at all. But a promise needs a partner. When the country your paper is heading to never made it, nothing on the British side can supply the missing half of the bargain.
Where Iraq stands
Iraq has not joined the Hague Apostille Convention. Its offices therefore keep the older arrangement, in which the receiving state puts its own officer between a foreign paper and any use of it. That is not obstruction, it is simply the system that was in place before the treaty and that continues wherever the treaty does not reach.
The Wolverhampton to Iraq route in practice
The British half is impersonal and identical for every destination. One national office covers the country, acts through the post, and has no counter in the West Midlands. It will mark a register copy, a court copy or a sheet signed by someone whose hand it can trace, then return the file the way it arrived.
The second half is where the two roads separate. Consular staff read the document rather than merely matching a signature, and they keep a record of what passed their desk. Because that stage belongs to the receiving side, its rhythm is set there. A paper tied to a start date should leave this city with weeks in hand.
Protecting the record while it travels
Two desks and several post rooms make a long chain, so think about which sheet you are willing to lose. A fresh certified copy from Wolverhampton Register Office is drawn from the same register and carries the same weight as the certificate in your drawer, and letting the copy travel keeps the family record where it belongs.