BilliBob
I don't think your assertion that you need to convert is true, based on their text at:
http://www.rainbowair.com/academy_JAA-CAA_PPL.htm
They clearly state: 'There is no conversion of licence when you return to the U.K.'
It looks like UKFT has teamed up with Rainbow Air to offer the course. My only word of caution is to look closely when you would want to attend. Some months the LA basin can be like flying in pea soup; which as a trainee pilot means only one thing: lots of days spent sitting drinking coffee.
Of course, its better to phone the club up and ask directly. The man I knew at Rainbow Air is a Brit called David Parsons. Nice chap, and he'll even pick you up from LAX if you ask nicely!