Yeah you can request one but they'll make you fight for it. I had an emergency c section with my first (and a very poorly baby) I didn't want to go through that again and assumed I could just tell them I wanted one with my second but they were forcing me to have a vbac, it was only when i got to 34 weeks and they thought something was wrong with my baby (there wasn't it was just a mistake with the scan) that they then told me I had to have a section, vbac was no longer an option. So i politely pretended to be disappointed! But every appt they sat me down and told me I shouldn't do it, there was so much pressure.
Saying that though if she's goes private she won't have to fight.