First person I saw medically when pregnant was my GP, who referred me to the hospital for antenatal care - wasn't given an option one way or another, he just filled out the form, but here all the care is centred around the Womens hospital, so it was the obvious (I would say only?) thing he could have put on the form...
Midwife at booking appointment discussed it with me when I said my preference would be for a natural hospital birth. She gave home as an option for me, but said it was still early to be thinking about it, and I would be at liberty to change one way or another until very late in pregnancy.
By the time I had made my mind up, I had my 25 week check and said to the midwife then that I would like to give birth at home, she wrote it in my notes, and that was that. I saw the same midwife (4th so far, 5th midwife at next appointment!) at 31 weeks, and she said she would formally change my booking at my 36 week appointment all being well still, and they will then drop off kit/give me on call numbers etc. at 37 weeks, and be on call for me from then onwards.
I've really found that unless you mention it to them - at 25 weeks with me I made a real point of saying I wanted to be at home, then at 31 it was more casual like "oh, well
I will be having him at home..." hint hint! - then they will just assume you will continue with hospital as at booking. I really don't think it is too late to plan and discuss and confirm it with them, up to about 36 weeks. If you get a nice midwife, either your usual or a stand-in, bombard them with questions and get it set up and confirmed as soon as you like!