Over the past few months I have seen and photographed lots of grey and grey-green flies like this one, but have not had much success with identifying them. However, the orange abdomen of this one gave me hope that I might be in with a chance of identifying it down to the genus or even species level. And, yes, a search through diptera.info showed a fairly good match with several species of Phaonia, in particular P. rufiventris, P. subventa and P. bitincta (all Diptera: Muscidae). I also came across some posts by Joke van Erkelens in this thread at diptera.info which indicate how to distinguish these species. But, unfortunately, my photos are not clear enough to allow me to do this, so I will have to stick with Phaonia sp. for the time-being, at least.
Photos taken in Whiteknights Park, Reading University grounds, Reading, UK, on 2009-10-25.