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The article mentions new build developments. A property developer must have approval to build, there is no legal right to build on acquired land. Approval comes from the local council, according to various local criteria (like, are local schools at capacity?). Therefore, they could conceivably require that property developers must obey these new rules to be granted permission ("do you agree to only sell to people who don't already own a home?").

The Brexit vote didn't carry any legal weight, either. Still got implemented.

council can block planning permission for new homes that don't have their chosen set of restrictive covenants, which are tied to the property in perpetuity, transferring from old owner to new owner at sale time

similar to HOAs in the US

(though they have no power to add them to existing properties)