A few days ago, I came across this unusual pupa in the long grass in Reading University grounds. I have searched through all the pictures in my reference books and through all the photos at ukleps.org and I have been unable to find any buttefly or moth pupae that look anything like it. Out of desperation, I did a Google search on "black and white striped cocoon" and that led me to this page at Symbiont Biological Pest Management Co and to this page at the University of California Integrated Pest Management Program. Both of these suggest to me the pupa might be that of an ichneumon wasp of the genus Hyposoter. The Checklist of UK Recorded Ichneumonidae lists 15 species of Hyposoter. A search on the web suggests that Hypersoter tend to be small black ichneumons with reddish abdomens, much like the ones I have been seeing all through the summer (see here, and here, for example). I think I'll take this a very tentative identification.
Photo taken in Whiteknights Park, Reading University grounds, Reading, UK, on 2009-08-30.