he wants to know how close he can fly to the ground, that is "absolute altitude"
Never heard or used the term 'absolute altitude' in 30 plus years of flying.
in SERA it says ‘height’ means the vertical distance of a level, a point or an object considered as a point, measured from a specified datum
And that specified datum would be the ground or the sea.
ATC use height and altitude (as well as flight levels) and whilst height is used when operating on QFE, it is to give you your vertical distance above your landing datum ie the ground at the airfield.
All UK mil pilots operate at low level using height (measured with a rad alt) which is agl or asl.