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).