One word, two different jobs
The word has escaped its meaning. It now gets used for any official mark that makes a paper usable abroad, which is understandable and unhelpful in equal measure, because the two routes hiding behind it are not alike. One ends with a single certificate from a single office. The other carries on to a desk belonging to the destination and finishes there.
For this pair of countries only the longer one is open. An apostille for Turkmenistan is not accepted, so a request worded that way is really a request for the consular route. Reading it that way at the start saves the week that otherwise goes on buying the wrong thing and learning about it late.
Where Turkmenistan stands
Turkmenistan has not joined the Hague Apostille Convention. That one point decides the rest: document legalisation for Turkmenistan runs through consular channels, and there is no purchasable item called an apostille issued in Birmingham for use in Turkmenistan. Nothing about your particular paper alters that, and no office can set it aside for you.
It also means an apostille from United Kingdom to Turkmenistan is not a shortcut that somebody better connected knows about. Membership is agreed between states, so it does not vary by city, by document, or by how urgent a case is. What does vary is how well you plan for the desks that genuinely apply.
What the British stage is for
The Legalisation Office at PO Box 6255, Milton Keynes MK10 1XX confirms that a signature or seal on a British paper belongs to a real public officer. It works by post and has no counter to visit, so the job travels as an envelope in both directions. The charge is £45 / document (standard postal); £40 / document next-day (registered businesses).
On this route that is groundwork rather than the finish. Its value is that the signature question gets settled before the file goes any further, which is exactly what a longer chain needs. Calling that stage the end is where timetables break — much more often than calling it by the wrong name ever does.
The part that is yours to get right
Vocabulary aside, the work in Birmingham is ordinary. You need a paper an office can act on, which usually means one signed by a public officer rather than by you. For births, marriages and deaths, Birmingham Register Office at Holliday Street, Birmingham B1 1TJ issues certified copies, so a fresh copy can make the journey while your own stays in a drawer.
Then settle the number. Each document carries its own charge at the British stage and stays a separate item all the way along, so ordering two copies at the start beats discovering later that two were wanted. That choice, and the time you leave for the consular desk, are the only real variables on a route whose shape is already fixed.