We've just come back from a holiday house full of battered children's books going back 40 years & from this would hugely recommend:
Gwynedd Rae's Mary Plain series - there are luckily at least 10 of them
Alf Proysen's Mrs Pepperpot stories - there's a collection out currently, so no need to haunt second-hand shops
Finn Family Moomintroll The Borrowers (Mary Norton) and The Rescuers (Margery Sharp)
Pippi Longstocking