The ATO bit, new i seen it some where (CAA web page how to stay legal)
FCL.140.A LAPL(A) — Recency requirements
(b) Holders of an LAPL(A) who do not comply with the requirements in (a) shall:
(2) perform the additional flight time or take-offs and landings, flying dual or solo under the supervision of an instructor, in order to fulfil the requirements in (a).
Flights may be either solo or dual.
CAA 'How to stay legal' web page only refers to the solo element which, although not mandatory at an ATO, is (as I previously stated) probably a good idea. Dual flying can be conducted by any suitably qualified FI - either inside or outside of an ATO environment.