I'm not familiar with situation in the UK, but in other countries there are NGOs that try to complement the national healthcare services, ranging from financing ambulances to at home care. They are often tied to religious movements.

At a quick glance, Hatzola Northwest seems to provide services for free to everyone in their catchment area, so any segregation is geographic in origin.

Nope, it is an adjunct funded by the Jewish community to avoid accidental things not approved of (can't list what as I can't recall).

Not exactly. The Orthodox Jews run their own service in a lot of places. https://en.wikipedia.org/wiki/Hatzalah

Two things:

1. It’s not restricted the the UK. Hartzola (the various orthodox Jewish ambulances services) operate all over the world.
2. Although they tend to be based in majority Jewish areas, they don’t restrict their service to Jews, as part of their code.