Thanks for both replies. I don't use Chrome and I don't have a Google account. I only use the site as a search engine.
As I said, it was the sequence that concerned me. Went on line as usual, went to about 6 sites for a scan read, then to FB. This was slow to load, albeit nothing strange about that, but then came the message asking for my password. I decided not to proceed at the time, but would do so later. It was when I went back to the previous sites I had opened up normally that the "log in / password" messages started to appear.
However, again, as I said, there was a Window's update later on and I'm aware these can cause glitches.
Everything now appears to be working normally, thankfully, but any IT issues concern me because I really don't understand IT other than the very basics.