Interesting discussion. Here's the relevant bit of the ANO:
SCHEDULE 7
PART A
Flight crew licences
SECTION 1
United Kingdom Licences
SUB-SECTION 1
Aeroplane pilots
Private Pilot’s Licence (Aeroplanes)
Minimum age – 17 years
No maximum period of validity
Privileges:
(1) Subject to paragraph (2), the holder of a Private Pilot’s Licence (Aeroplanes) is entitled to fly
as pilot in command or co-pilot of an aeroplane of any of the types or classes specified or otherwise
falling within an aircraft rating included in the licence.
(2) The holder may not—
[...]
(g) fly as pilot in command of such an aeroplane carrying passengers unless—
(i) within the preceding 90 days the holder has made at least three take-offs and three
landings as the sole manipulator of the controls of an aeroplane of the same type or
class; and
(ii) if such a flight is to be carried out at night and the licence does not include an
instrument rating (aeroplane), at least one of those take-offs and landings has been at
night.
So you cannot act as PIC of a passenger-carrying aircraft if you haven't done the three landings in the last 90 days.
So you somehow have to chalk up those landings, either as a solo pilot (PIC, but not carrying passengers) or in a position where you are not PIC, but you are the sole manipulator of the controls. This can be done with an instructor (he is PIC, you are PU/T) but, indeed, I can't find any legal reason why this cannot be with another current PPL (he is PIC, you are PAX but manipulating the controls).
This would seem to me to be fairly conclusive as a Safety Pilot is not permitted.
The carriage of a safety pilot is not something that the ANO specifically allows or forbids, for the simple reason that the whole concept of safety pilot is not defined in a legal sense (*). For legal purposes, the safety pilot is just a passenger and since you're not allowed to take passengers, you can't take a safety pilot either.
(*) Except within an article about simulated instrument flight. And the definition is then limited to that context.