Where Turkmenistan stands
Turkmenistan has not joined the Hague Apostille Convention, so an apostille for Turkmenistan is not the mark that finishes a paper used there. Embassy or consular legalisation applies instead: the FCDO Legalisation Office certifies the document, and a consular stamp is added afterwards. Reading that as two errands rather than one long delay is what makes the corridor manageable.
The one part that is strictly in order
The consular desk looks at what the British desk has already done, so the second stage cannot be started, booked forward or half-prepared on the paper itself. That single dependency is the whole of the sequencing on this route. People treat it as though the entire job were a queue, and then sit still for weeks waiting for permission to do things nobody was going to stop them doing.
What can be done while the first desk works
Copies come first. A register office visit that produces every certified copy you might need costs one afternoon, whereas a second visit costs a week of post on top of it. The same applies to school and company papers, which come from the bodies that issued them and can be gathered while the first envelope is somewhere on the road.
Then there is the plain admin nobody schedules: who receives the finished set, what name and spelling appear on each sheet, and whether the person abroad was asked for one document or three. None of that waits on a stamp. What you need for an apostille for Turkmenistan is not a checklist for the first stage; it is a habit of using the dead time the route hands you.
Time you spend once, not twice
The British charge falls on each document rather than on the envelope, so the count you settle early decides that half of the bill. Those rates are printed; the consular charge is set by the desk abroad and no figure for it belongs here. Doing the loose work early speeds up neither desk, but it stops you paying for a second run through both.