Who books my practical driving test?
It could be you or your instructor.
Who books your practical test does not make much difference as long as it is not booked before you are ready for it.
Some instructors insist upon booking your practical test themselves whereas others are quite happy for you to book it yourself. If you have a particular preference then you should make your instructor aware of it.
Personally I insist upon booking my pupils tests so that I can make certain that I am never double booked with driving tests.
Findley's Driving School offers its instructors a centralized booking service so we will book the tests for them if they so wish. Whichever way it ends up being booked your test should not be applied for until your instructor says that you are ready to take it.