Ahh quote from the Pimlico website
"All Year 12 students have a full timetable of at least three A Levels and an additional accredited activity.
Pimlico Academy Post 16 is a part of a consortium arrangement with other schools and colleges in Westminster including The Grey Coat Hospital School and Westminster City School. Students are able to take at most one subject in a Consortium School or College."
State and private schools working together seems to be increasingly common in London, supported strongly by some local authorities who often take the initiative in getting senior staff round the table. More obvious examples are Harris Westminster supported by Westminster School and Hammersmith Academy, which has strong links with St Pauls Girls and Boys schools.
From observation there seems to be several obvious areas of joint working, including music, sport, smaller subjects including MFL, teacher INSET training perhaps on things like SEN support, Oxbridge applications, STEP preparation, management and administration, etc. And that the traffic can be two way, with all staff involved having a chance to broaden their experience and understanding.