In a nutshell, from an ICAO CPL to gain JAA CPL, you need to pass the ATPL or CPL exams, training as required plus pass CPL skill test. A JAA IR has to be done in JAA-land.
You will then have a JAA CPL/IR, not an ATPL which requires 1,000 hours plus other experience requirements.
Please be careful when people say ATPL; they usually mean ATPL theory credits which is not the same thing.
Download LASORS from the caa website; all the info will be in there.
Cheers
Whirls