When I did my ATPL the BA "approved list" for the self-sponsored pilot programme was:
Oxford Air Training
West Michigan University IPTC (where I trained)
BAE Systems – Jerez/Adelaide
Cabair - Cranfield
NLS – Netherlands
KLM Academy – Netherlands
Lufthansa Flight Training
European Pilot Selection and Training (EPST)
Not sure if all of these are still in business, but probably academic now anyway!