"The MetropolitanOpenLand surrounding Hampstead Heath is an important buffer between the Heath and the surrounding built environment, " a spokeswoman said.
But when granting permission, council officers said the MetropolitanOpenLand that would be affected was the garden of the building itself, which was not open to the general public.
The new building, described by the council as being of a modern design with "a succession of cube-like shapes superimposed on each other", would cover a wider area - including some MetropolitanOpenLand.