It's the same in the UK for the most part.
OpenReach (which was "split off" from BT) puts the infrastructure in place, and OFCOM (our telecoms regulator) defines the price they can charge to ISP's for a connection - so you have a raft of ISP's who compete on price or service.
There are other infra providers though, Virgin Media (DOCSIS Cable) cover some of the country, CityFibre are doing a massive expansion (I now have all three available at my property), Hyperoptic (mostly focuses on apartments).
And then there's Hull ... which is a special case that never became amalgamated to BT back in the day and instead is served by Kingston Communications.
For the most part it works well, but heavy regulations is anethema to some over the US side of the pond and therefore YMMV.