Nick,

ANO article 32 applies to ICAO-compliant licences which are valid all over the world.
33 covers the medical requirements for the NPPL which only confers rights within the UK.

In addition to reading your training manuals, it’s a good idea to become familiar with the source documents. That’s mainly CAP393 which can be downloaded from the CAA web site.
The UK AIP is most easily accessed from the NATS AIS sight recently moved to http://www.nats-uk.ead-it.com the AIP is available without logging in, but you will need to register sooner or later in order to get NOTAM access for cross-country and local area flying. It’s free anyway.

As for explaining JAA and EASA, it is believed that as soon as somebody understands it, it will be replaced by something even more bizaar and confusing. It is also believed that this has already happened (with apologies to Douglas Adams).