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.