The due date is the only fixed point
Most people start at the wrong end. They want to know what to do first, get a list, and work through it at whatever speed the week allows. The day the paper is needed then arrives as a surprise. Turn it round: write that day down first, and let it decide how much of this you can do calmly.
The order matters more here than on a short route, because the finish is not in Britain. An apostille for Malaysia is not accepted there, so the file has a consular stage after the British one, and each stage brings a wait of its own. Counting them early is the difference between a plan and a hope.
Why this route has an extra desk
Malaysia has not joined the Hague Apostille Convention. Because of that, document legalisation for Malaysia runs through consular channels, and the last word on your paper is said outside Britain. There is no shorter version on sale, and no finished item called an apostille issued in Birmingham for use in Malaysia.
This is settled between states, not by whoever opens your file. So looking for an apostille from United Kingdom to Malaysia leads back to the same answer every time. The British stage is real and worth doing well, but it sits in the middle of the job rather than at the end of it.
Nothing starts before the paper exists
The first wait is the one people forget, because it happens before any stamp. A record has to be in your hands in a form an office will act on. For births, marriages and deaths, Birmingham Register Office at Holliday Street, Birmingham B1 1TJ issues certified copies, so a fresh one can be ordered while the record you keep at home stays at home.
Order the full number at that point. The British charge is £45 / document (standard postal); £40 / document next-day (registered businesses), and it follows each document rather than each envelope. If two people abroad will each keep a stamped paper, that is a decision for now, not for after the file has travelled.
What speeds up, and what will not
Only one part of this timetable has a faster setting, and it is not open to everyone: the next-day charge at the British stage is for registered businesses. The rest runs at the speed of post and of desks you do not control, which is why a calendar has to absorb the wait rather than fight it.
So the levers you really hold are early ones and simple ones. Start the copy sooner. Decide the number of copies once. Keep the due date in front of you while you do both. A route with more desks is not harder to run — it is only harder to rush, and the cure for that is time you gave yourself at the start.