often seen in the street without a hat

I think those are pretty good! I find Molly Hughes a little irritating, and her schooldays are retold in A London Girl of the 1880s rather than the 1870s book, but that's my only reservation.

I really love Greenery Street, and Miss Pettigrew Lives for a Day is the one that gets recommended most often. Family Roundabout is good too - though not very like Just William.