There was just the one fair weather base in the USA near Phoenix
B61 - yes, albeit almost 20 years ago but concurrently there were fair weather bases in Florida at Lakeland (KLAL), Pompano Beach (KPMP), and for a time Vero Beach (KVRB), and in Arizona, Deer Valley (KDVT) and Williams Gateway (KIWA) all primarily tasked with training sponsored cadets from BA/BD/EI and others as well as self-sponsored long-course (integrated) students. Remarkable to think that at that time, only about one-third of the current syllabus was conducted overseas in terms of flying hours with SE CPL and ME IR (in fact almost all instrument instruction) delivered at Kidlington. Following some consolidation just pre and more significantly post 9-11, all of the fair-weather training moved to Tyler (KTYR), Texas following OAA's acquisition by BBA and capitalising on existing facilities there (Signature Flight Support). The weather was not really suitable for sustained year round VFR training however and an arrangement with a Belgian owned FTO (SFA/SATC) operating their own FWB in Scottsdale (KSDL), AZ resulted in a return to the Phoenix area which subsequently lead to the establishment of the Goodyear (KGYR) operation with facilities leased from Lufthansa (ATCA) for a number of years and following purchase by CAE, the entire operation was assimilated into their 'Global Academy' facility at Mesa Falcon Field (KFFZ), which is where the students are sent today. Madrid, Brussels, Evora and Amsterdam all existed as CAE simulator centres previously, with a facility for ATPL theoretical knowledge training at each and students farmed out to FTO's for practical training although now of course, they go to KFFZ.
The modular school in the UK I referred to was at Gloucester around 2000-2001 with it's own CFI and dedicated instructor team. They had a fleet of Seneca III's (the Kidlington ones were II's) and away from the busy Oxford environment, was a good little operation. IIRC, there was also something at Carlisle for a time as well and perhaps a little earlier. Sad to see the name go and as you say, we could well be moving towards a time where any meaningful training is simply impractical as EGTK becomes another Biggin Hill. The apron certainly doesn't look anything like it did a few years ago but some would call that progress I suppose. Happy days!