It looks like we had a lot of overlap in our reading! I was a massive Chalet School fan and still have a full reread of the series now and then. Other ones that still come out for rereading include the Drina and Sadlers Wells books (I only had the first five as a child, I have a full set now but given how much the quality nosedives after the first few I don't think I missed much!), the Jill books (again, I only had a few as a child but have since acquired them all), Anne of Green Gables series and the first three Katy books. I didn't have all the Noel Streatfeild ones but did have Ballet Shoes and The Circus is Coming (funnily enough the combination of the original thread and seeing a circus tent near Turnham Green while passing on the tube led to me rereading that on Wednesday), and later got the Gemma books too - also, when I was in my first school we started on When The Siren Wailed but my family moved before we'd got very far (army life!) and I didn't get round to reading it until I was an adult.
Others that sprang to mind last night while I was turning this over in my head include the Narnia books, the Famous Five (again, I was a massive fan of these - I read a few of the Secret Seven but they never gripped me in the same way) and also the Malory Towers (...although I always had a sneaking suspicion that the character I was most like was Gwendoline) and St Clares series. Five Children & It (and the Phoenix/Amulet sequels), The Railway Children, Carrie's War. Some of the Roald Dahl books. Sweet Valley Twins was my guilty pleasure at one point but I tended to read the library copies rather than have any of my own, so I haven't really revisited them as an adult - Babysitters Club likewise. Saddle Club books - that's another one where I had a few as a child but have acquired rather more since! I expect if I went upstairs and studied our bookshelves I could probably find more examples, we have a shocking amount of children's books for a childfree couple because I hate throwing things out and often get the urge to reread things.