I can't speak about the legal aspect of Turkey laying claim to water that lands on say, UK soil as I'm not familiar with the legalities involved.
However, the infrastructure to pipe water from the UK to Turkey is not in place. The cost of linking the countries via such a pipe would surely be prohibitively expensive even with EU support. Furthermore, I can't see that the environmentalists would be very happy about digging up large tracts of land through the countries in between Turkey and the UK. Who would pay for the upheaval in the countries involved?
I think we have to put the matter into perspective and admit that much of what the article cited mentioned goes on in fairly adjacent dictatorships in Africa, where law as we know it is virtually non-existent. If they want to ride roughshod over their neighbours they simply get on with it and most of the time assume a conflict will result.. Such behaviour will get them the water in the end although the price is horrifying in terms of both currency and human suffering.