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I looked into this a while ago, and it appeared that there were some misleading public announcements from CAA which indicated this 'LAPL privileges only'"
Those weren't misleading statements. The acceptance of UK non–Part-FCL licences, ie so-called national licences, on EASA aircraft was based on a derogation in art 12 para 2a(3) of the Aircrew Regulation that lasted until 8 April 2020, before being deleted by Commission Implementing Regulation (EU) 2020/359. The derogation limited the exercise of licence privileges to that of the LAPL. The UK CAA notified its adoption of the derogation in ORS4 No. 1309 (
pdf copy) published 12 Jul 2019, in addition to earlier notifications in ORS4.