I have experience of a termination after 20 weeks and a medical management of a mmc at 14 weeks.
I think that some hospitals will refer you to Marie stopes or similar for a surgical procedure up to 16 weeks. My hospital won't offer digital after 13 weeks, I didn't ask about a referral as I wanted a medical management.
22 weeks was pretty much like a short labour.
However, 14 weeks I was induced using normal induction drugs, given pain relief and used gas and air. It was a little bit like labour. There are lots of women here who have had the same thing and only needed mild pain relief.
I opted to go to the delivery ward but this was more uncommon (I wanted to have a similar experience to my dd2 and I knew the midwives were amazing with still birth and mc there) usually you go to a private room on the gyne ward.
You can opt to see the baby. We did in both circumstances but only because I knew it would help me grieve. We have photos, hand and foot prints and a memory box for both babies. Both of our babies are named and we have/will have them cremated. For me it was a way of completing a circle.
That is my experience. You experience doesn't have to be anything like that. Generally hospitals will do all they can to find the best way for you.
I will say whilst I was going through my tfmr I was utterly terrified of giving birth to her (I had no choice that late on) and I had already had my dd1. However, it wasn't as hard or as scary as I had imagined and strange as it sounds birthing her (and also my ds) has helped the healing process.
If you are definite that you want a surgical procedure and the hospital can't do it I'm pretty sure you can go private up to 16 weeks too. Don't quote me on the 16 week mark but I'm pretty certain it's the cut off for surgical.