Right, latest report.
I did nothing except switch it off, go to bed and boot it up again this evening, and now it's working perfectly again.
The wonders of computing.
For those who are interested, I was having no other problems associated with internet usage, speed was apparently normal. Other videos (presumably not using Flash) played perfectly. The weird thing was that the YT thumbnails/stills would display fine, but when clicked-on, the user controls which are normally available underneath it the YT screen (play, pause etc) did not appear. The screen stayed black.
Thanks for the suggestions!