JAFO, you're right. It is even more complex at the moment.
Callum, EASA is taking over Flight Crew Licensing from the various European regulators such as the UK CAA, but only where it applies to "Annex I" aircraft. "Annex II" aircraft will, for the moment, remain under the national regulators, and under national rules for Flight Crew Licensing. In other words: For Annex I aircraft the EU legislation is law, for Annex II aircraft the ANO is law.
Annex I aircraft are essentially aircraft with a full Certificate of Airworthiness, from the lowly C152 to the B747 and A380, while Annex II aircraft are essentially microlights, experimentals, homebuilts, vintage, ex-military and various other aircraft at the low end of the market - although that last statement doesn't say anything about their performance. There are Annex II aircraft out there that will run rings around a lot of Annex I aircraft, in performance, build quality, safety and everything.
Anyway, to fly an Annex I aircraft you need an EASA license. To fly an Annex II aircraft you need some sort of national license.
All current JAR-FCL compliant licenses are being converted to EASA licenses automatically, and all new licenses will be EASA licenses by default - unless you are specifically applying for a non-EASA license. Furthermore, I believe the CAA implicitly validates EASA licenses as equivalent to national licenses, meaning that you can fly Annex II G-reg aircraft on an EASA license. Other EU countries are by and large doing the same, I think.
However, the NPPL is a UK specific license and doesn't come with an automatic upgrade path to an EASA license (LAPL or otherwise). This means that the NPPL will only allow you to fly Annex II aircraft in the near future - even though you can currently use it to fly Annex I aircraft already. There are various threads on here, and there is information from the CAA, on what you need to do if you're an NPPL holder and want to keep on flying Annex I aircraft in the future. CAP 804 is supposed to be your friend.