Held on behalf
Section 3(2)(b) of FOIA states "For the purposes of this Act, information is held by a public authority if ... it is held by another person on behalf of the authority" 
There is a relevant ICO guidance note  which gives the example of research material being held by another.
This ICO decision notice  is particularly relevant, where market research response data held by a private company was deemed to be held by the 3rd party on behalf of the public authority, and the Information Commissioner partly upheld the Section 3(2)(b) appeal.
 FOIA 2000