Thanks for all of the advice. Fortunately a colleague had just upgraded his graphics card and gave me his old gtx690 which I installed and hey presto - working perfectly. So problem solved, plus I get an upgrade to my gfx card into the bargain.
In the past few days my screen looks like the attached pic. The lines are there constantly, though they do move around a bit, and occasionally there are sections (eg some text input boxes) where they disappear, but basically it's always like the picture. I have tried DDU and changing graphics...