Korda is not entirely right.
Radar in 1940 could determine altitude reasonably accurately. If you find a good image of the
receiving towers of a Chain Home station you will see the two dipole antennae at different heights (215' and 95'),which were used to do exactly that. In ideal conditions the terrain should be flat for a mile in front of the antennae (for technical reasons I'm not going into here). The system was calibrated for each station with a large number of calibration flights. Chain Home could certainly measure altitude.
Again, for technical reasons, detection at high angles above 8 degrees could be problematic and required an experienced operator to be exact. Fortunately most detections occurred at ranges where this was not an issue.
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Once across the coast the Observer Corps used basic instruments and trigonometry to determine and report altitude.
Dowding never assumed anything. RAF Intelligence compiled reports on the structure of German formations, including the altitude of the bombers, disposition of escorts etc. throughout the Battle. I know because I have read some of them!