They are said to be cohabiting, or just 'living together'

They're a couple or they're living together.

It's called civil partnership on the GOV.UK site. https://www.gov.uk/convert-civil-partnership

De-facto/de-facto relationship

Hi :) In my country, South Africa, we usually just call unmarried couples partners. But often, even if people aren't married, they still refer to their partner/spouse as their husband or wife. :)