HD
I should point out that he meant nothing like that-quite the opposite in fact that he was frequently only cleared to 6000 quite properly to stay beneath the inbounds headed for Ockham.
As to altitudes i have often depatrted LHR on both these routes and it seemed quite common at busy times to stay at 6000ft until past Biggin let alone Epsom and much the same going north to stay below Bovingdon
PB