I was assigned an atrocious midwife for my induction last year, and after about 20mins of not being able to relax, my mum went to the midwife in charge and asked for a change. I was accomodated very well.
I would suggest you talk to the midwives about it - if nothing else they will more than likely give you a "better" midwife if there is no choice re the OB, to compensate. Does that make sense?
So even though you are public, you should have a right to state your preference, particularly if you have had unpleasant experiences in the past.
I'm sure the midwives have met similar requests and know exactly how to handle it.