The CAA certainly do publish a list of approved centres. If they didn't, how would anyone know who was approved to do what? It's incredibly strange that they would say on the phone that they don't, but then it tells you everything you need to know about the CAA helpdesk.
Open the PDF and search for 'Assessor of Aviation English Language Proficiency'.
http://publicapps.caa.co.uk/docs/33/...sion%20153.pdf