This is not correct, we have both much like the US.
We have unions for a particular company for example, here is the Wikipedia link for the Nationwide Union, a building society. https://en.m.wikipedia.org/wiki/Nationwide_Group_Staff_Union
Certainly over time they will consolidate, but that goes back to my point about age. If other warehouses unionise, at some point they will group together to prevent the closure of warehouses just because Amazon doesn't like the people working there.
I understood the US has the same situation, with groups like United Farm Workers or the Federation of Teachers.