Update.
Today I went back to the house to check the job over. She wasn't kidding about the spotting. It was awful. I never doubted that she had a point as she;'s not normally a picky customer. Anyway, she was in. I started to go over the windows with the applicator and squeegee and the spots seemed to be really ingrained into the glass. It was as if I had left spots on there first time and the second clean didn't touch them. I got them off eventually with the help of a washing up pad. She wants me to continue cleaning for her (I wasn't bothered one way or the other about this as I don't earn enough from it).
The way I left it was that I got all the spots off and finished off two of the ground floor windows with WFP as an experiment. On one of the windows I scrubbed above the frame (again). On the other, I just did the glass. I want to see what happens to it. She will phone me tomorrow to let me know how those two look.
I nearly got lumbered with doing the landing windows above the flat roof until I noticed the overflow pipes above them. The spots on them are badly ingrained but they're not my spots
.
Anyway, the frames are the old metal double glazed type with wooden surrounds. Also, above some of the frames, a concrete lintel shows on the outer skinn of brickwork and is painted. I'm wondering if I've scrubbed this too and something has seeped out. I intend to get to the bottom of this by the process of elimination. If I'm not able to, then I guess that this will end up being a ladder job (no reasonable alternative if mystery spots keep showing up).
I even checked for hanging baskets nearby as I've known glass to get spotty when people water them - but no such luck.