A visit to the CAA website LASORS section still does not make it very clear what I need to do.
I doubt that they will know. The rules say that your ICAO licence is valid worldwide, the UK accept licences from all other States without question. What the other States do is up to them, even if it is contrary to the agreements they are signatories too. The tricky bit is JAR-FCL 1.005 (b)(3)
Holders of a licence issued in accordance with the national regulations of a JAA Member State before 1 July 1999, may apply to the State of licence issue of the equivalent licence specified in JAR-FCL1(Aeroplane) which extends the privileges to other States as set out in JAR-FCL 1.015 (a)(1) - this only states that all JAA States will accept a JAA licence.
ICAO Annex 1 States:
1.2.2.2 Recommendation.— A pilot licence issued by a
Contracting State should be rendered valid by other
Contracting States for use in private flights.