The certificate that does not travel here
Iraq has not joined the Hague Apostille Convention, so the single-mark route that Convention countries rely on does not apply to this corridor. An apostille from United Kingdom to Iraq is not the finished article a receiving desk over there wants to see. What stands in its place is a chain of two: a British certification stage first, and a consular stamp added afterwards on Iraq's behalf.
The weeks the paper is not yours
From the moment the envelope is sealed until the second stamp is dry, the sheet belongs to a queue rather than to you. The British stage is worked entirely through the post, and the consular stage that follows is a separate handover with a timetable of its own. Nobody passes the document back to you in between the two.
That matters whenever the same paper is wanted for something else — a tenancy file, a school place, an employer's check. Work on the assumption that it is unavailable for the whole run. Where a second copy can be obtained without difficulty, obtain it before the first one goes anywhere near a postbox.
Choosing the sheet that goes
Civil records have a real advantage on a route this long: the entry stays in the register whatever happens to the paper, so another certified copy can be printed later. The register office at the Civic Centre does that for births, marriages and deaths recorded in the city. A degree, a company file or a signed statement has no such register standing behind it, and replacing one means going back to whoever issued it in the first place.
The charge you can name, and the wait you cannot
The British charge is £45 per document by standard post, or £40 per document on the next-day service open to registered businesses, so the bill follows the count of sheets rather than the weight of the envelope. The consular stage carries a charge of its own, set well away from Britain, and there is no honest way to quote a figure for it from this side.