A blog post explores some of that organization's records at TNA in this the WI's centenary year. The Women’s Institute: it’s not all jam and Jerusalem mentions that the National Federation of Women’s Institute and Denman archive is held by the Women’s Library, at the London School of Economics and Political Science Library.
The WI material seems to be single images such as this one of the first WI building.
While developing this post I wondered about the institution in Canada, and specifically about the OGS plans to digitize the Tweedsmuir Histories as announced in November 2009. It was supposed to be a three year project. It appears this was seed that fell mostly on stony ground. That's unfortunate although a few are linked from the Federated Women's Institutes of Ontario site at http://www.fwio.on.ca/tweedslinks.