. . . erm, an EASA licence is valid for non-EASA aircraft (at least in the UK.)
True. However, you need to understand the legal situation.
EASA does not set rules wrt. to non-EASA aircraft. It's up to the local authorities to set rules for maintenance, licensing and whatnot.
The UK has decided that you can fly a non-EASA aircraft either on the appropriate EASA license (EASA LAPL, PPL, CPL, ATPL), or on the appropriate UK license (UK NPPL, UK PPL and so forth).
In the UK you can therefore hold both a non-EASA license (eg. NPPL), and an EASA license (eg. LAPL) for the same class of aircraft. But you cannot hold two EASA licenses (eg. LAPL and PPL) for the same class of aircraft.
Other EASA countries might not issue or support non-EASA licenses anymore. In those cases, the only license that the local authority allows to fly a non-EASA aircraft, is an EASA license. But that's something that's written down in local law, not in the EASA legislation.