OK folks - I'm touching wood here, but I think I may have resolved the problem. I've undertaken a few measures, as recommended on various forums, so I don't really know which measure worked. However, fingers crossed!
So here's what I did:
- Because the problem may have been associated with the latest version of Java Runtime (I kept getting pesky pop up messages to install it, when it was already installed), I followed someone's advice and downloaded and installed Java 6. This has certainly stopped the pesky pop ups, which may or may not have had something to do with the Safari issue;
- next I deleted the file~/Library/Caches/com.apple.Safari/Cache.db, as recommended by someone else;
- finally, I ran disk repair (it was OK) and Permissions repair. Now, there were umpteen and a half permissions that needed repair following the Yosemite update, mostly related to my printer, but others too.
So that's it. The computer has been left unattended for an hour or so, has gone to sleep, had been rudely reawakened, and the problem seems to have rectified itself.
It's early days, so I'll be back to tell you if my optimism was misplaced!