I can't speak for sure about British English usage, but in the United States we wouldn't use the verb "to book" in this context. I would say "they've ordered a pair specially for me." Note: On second thought, I do agree with Nanren888; "specially" is correct here, so I've made that change to my original answer.

You would not use "booked" in this situation, even in Britian. To "book" something is to "arrange" or "schedule" something, such as an appointment or a flight or even a restaurant reservation for example. In this situation however, the action (verb) being carried out is not one of scheduling; rather, it is the act of procurement - obtaining something (shoes) for you. Hence, you would say "ordered" as Sheila suggested, or "requested" or "commissioned" (formal). Just to note, when the other store then delivers to your chosen store, or to your home, then they will "book a delivery" ;-) I hope that helps!

ordered a pair (specially) for me ordered me a pair . Can you use "book" like this? No. Not an understood or used meaning.

Even though I understand what you mean, you wouldnt use that term referring to shoes. You would use booked for things like flights or hotels. "I booked a flight to europe" or "I booked a hotel for 2" booked is term for like reserving something. Hope that made sense.