That's because there's no conversion process whatsoever.
You can fly a G-reg aircraft on any (current) ICAO PPL (or higher), worldwide without any formal validation process. The details are in the ANO and/or LASORS, but you are generally restricted to PPL privileges and Day VFR.
LASORS: LASORS 2008 | Publications | CAA Section A7.
It's a good idea to do a flight with an instructor first, though. There are a few things peculair about UK airspace, such as no closing of flightplans, ATSOCAS, PPR for most airfields, overhead joins, MATZ transitions and a few others.