Check
www.easa.europa.eu/faq/121071. It isn't a complete answer to your question because it doesn't discuss G registered aircraft.
Also
www.aopa.nl/index.php?page=1318&sid=1 (in Dutch). Aopa asked your specific question to the UK CAA. No answer mentioned yet. It does have an email address for questions.
edit:
This has your answer.
info.caa.co.uk/uk-eu-transition/private-pilots/
Specific chapter with Q/A on LAPL.
Conclusion: No flying outside of UK airspace with a UK issued LAPL. Or inside UK airspace with a EU issued LAPL.