Do you have a reference that states that the same thing applies to the LAPL?
No, thats what I was looking for, but conversely there is absolutely nothing to say that you cannot. FCL040 is the only reference and that states that the licence privileges are predicated on the basis of the aircraft rating and the medical, nothing else. If you read through the Part FCL privileges of the various licences you will see the cascading down is evident they just haven't spelt it out in the PPL. If an ATPL or CPL holder can exercise LAPL privileges there is absolutely no reason why a PPL holder cannot. As you have a lifetime licence, they will not issue you with another lower level one as there is no need to. You could of course upgrade it if you wanted to.
I am fully aware there was no NPPLL (H) however there is now provision for one! ANO Schedule 7
National Private Pilot’s Licence (Helicopters)
Minimum age – 17 years
Privileges and conditions:
(1) Subject to paragraphs (2) to (4) the holder of the licence is entitled to fly as pilot in
command of a single-engine helicopter with a maximum total weight authorised of
2000 kg or less, carrying a maximum of 3 passengers, such that there are never more
than 4 persons on board.
I simply used this reference to indicate that it was the exception rather than the rule and the only case I know of where cascading down was deliberately omitted for political reasons. The ORS was to alleviate that restriction.