Just to re-iterate - If you are flying an aircraft on the basis of your UK issued JAA PPL (or, indeed, UK national PPL), the privileges of that licence are detailed in the ANO. This applies no matter where in the world you are flying nor in what state the aircraft is registered. If, however, your UK issued PPL has been validated in another state (or 'converted' if you speak american) then it is as though you held a licence issued by that state and the privileges are those laid down in the validating state's legislation.
The JAA PPL, and CPL for that matter, are VFR licences. The privileges do not entitle the holder to fly in a visibility of less than 3km or out of sight of the surface. The privileges of a CPL are, essentially, those of a PPL with night qualification (leaving aside the matters of remuneration and public transport).
In order to fly IFR it is necessary to hold an Instrument Rating or (in the UK only) an IMC rating. However, the IMC rating is not recognised by any other country and, therefore, its privileges do not extend outside UK airspace. No credit will be given for holding a FAA Instrument Rating in any JAA member state other than the UK as there is no equivalent to the IMC rating.