I'm by no means sure, but here's my best guess: Escher's Blue, Agrodiaetus escheri.
It is a brave or foolish man who dares query an identification by Florin, but after a lot of hesitation I am going to do just that.
I was immediately suspicious of the identification because what struck me about the underwing shot was the prominent blue flush at the base of the wing. I don't think that Escher's Blue has such a prominent flush and studying the photos in the two links provided by Florin has not persuaded me otherwise.
Then again the upper wing does not look entirely like Esher's. Study the photos in the links and you will see black lines running quite some way way from the costa along the veins, as if black ink has run along the channels. (Look at the large photo on the right in the butterfly-guide.co.uk website.) I see some black lines running back from the costa in the upper wing picture of the unknown specimen but mainly these are between the veins and not on them.
I'm going to stick my neck out and suggest this is the Common Blue. I hestitated to come to this conclusion because my field guides show a much thinner black line around the costa than in the unknown specimen. However, varations do occur within a species and I found an image on the internet claiming to be a common blue with a thick black line round the costa.
The common blue does have a prominent blue flush on the root of the underwing as in the photo of the unknow specimen.
Thanks for your thorough examination of this. The Common Blue was the only one I considered instead of Escher's. I don't totally agree with your first observation: it seems to me that our mystery insect has the same blue flush at the base of its hindwings as the Common Blue. The Escher's Blues on this page also have the same feature. Our image is a bit underexposed, so you would need to add brightness, or as I did, to darken a bit one of the Escher's photos to make a comparison. Here is an Escher's from eurobutterflies website, a bit darkened by me:
I think the blue is there. However, I'm not sure about your second observation, the upper wings. I simply don't see very well those fine differences, so I guess you are right about that.
Too bad the butterfly didn't open a bit its wings so we can see a better character, the black spot in the underside forewing cell that is absent in Common Blues. Well, most of the times.
In my book, Escher's Blue has paler underwing backgound colouration than the Common Blue, and that made me lean towards the former. However, looking at many photos of these two species, it doesn't look like a very trustworthy character anymore. In fact, almost all of the best, clear-cut characters that separate the two are contradicted by at least one of the photos posted on the very pages that use them to illustrate the ID!
Bottom line: I really don't know which of these it is, and your analysis makes me lean now towards the Common Blue.
I will ask an expert to take a look at this thread and I hope I will get his opinion soon.