It's a very vague memory but I know I loved reading the book (or possibly books, there may have been several) at school in the early 90s. There were no people in them, just an anthropomorphised dragon family wearing clothes, going to school etc. They were a similar level to to the Allan Ahlberg books, but definitely a different author. Lovely colourful pictures.
I've googled the heck out of it but to no avail - I just don't have enough detail to do a good search. I think it needs someone to go "Yes! I remember that!", hence giving in and posting here 