Two figures, not one
Britain publishes two charges for this work. The standard postal route costs £45 per document and is open to anyone who writes in. The next-day route costs £40 per document and is meant for registered businesses. The faster line being the cheaper one catches people out, because it was built for firms sending papers in volume rather than sold as a premium.
What a line actually covers
A line describes what happens inside the Legalisation Office, which works from PO Box 6255, Milton Keynes MK10 1XX. It says nothing about your envelope's journey there, or its journey home. Those legs run at the speed of the post and are the same legs whichever figure you paid, so counting them on their own is the only way to land on a real date.
The choice has no effect on the sheet you get back either. Both routes produce the same slip from the same office, and nobody reading the file later can tell them apart. What you are choosing between is a clock and a charge, not two grades of mark.
What neither line reaches
Turkmenistan has not joined the Hague Apostille Convention, so document legalisation for Turkmenistan does not end when that envelope comes home. An apostille from United Kingdom to Turkmenistan is followed by a stamp from Turkmenistan's consular staff in Britain. Neither British line reaches into that office, whose charge and whose timetable sit wholly on its own side of the job.
Building a plan around the fixed part
So what you need for an apostille for Turkmenistan is a signed public version of each paper, the right line for who you are, and a separate slot for the consular half. Westminster Register Office at 317 Harrow Road issues fresh certified copies of civil records, and ordering one is the block that people leave last and ought to start first.
The result is a three-part schedule with one dependable piece in it. Getting the paper signed is yours to control, the British stage is published and predictable, and the stage after it is neither. Treat the middle as the fixed point and build the days on either side around that.