I think it's not just British, but a very European way of handling pregnancy, not having too much medical involvement unless there are problems at the start of the pregnancy. I haven't been pregnant in Sweden (too OLD), but my younger friends always talk about how they feel they aren't seeing the doctor enough, aren't getting vitamins and other meds shoved at them, etc. A lot of the care in the United States is too much care fueled by fears of medical malpractice lawsuits, a cover your ass philosophy so if anything at all happens, they have tons of medical records to show that they did everything possible, even if it wasn't necessary. Most of my friends here have been delivered by midwives, even some at home, and have ended up being pleased by the handling. May you have the same excellent care and a safe delivery.
It IS always stressful when you are far away from your home ground and your first pregnancy. On the other hand, perhaps you miss a lot of the horror stories that a great many mothers feel they have to tell the first-time pregnant lady, along the lines of being in dry labor for 87 hours and then delivering a 60-pound baby, etc., most of which is total rubbish. I never did understand why a lot of women had to do that to each other.