WhatDoTheyKnow is an excellent website that allows you to make,check on and search Freedom of Information (FoI) requests in the UK.
Some of those FoI requests concern art.
Art organizations:
http://www.whatdotheyknow.com/search/art/bodies
The National Gallery:
http://www.whatdotheyknow.com/body/the_national_gallery
The NPG:
http://www.whatdotheyknow.com/body/the_national_portrait_gallery
And of course The Tate:
http://www.whatdotheyknow.com/body/the_tate_gallery
It’s interesting to see not just the answers but what kinds of things peopel are asking which organizations about (and whether they’re answering).