I am sad to say that I can't remember the names of the books that I read as a child. But I do remember being in about third or fourth grade, and we had library day every Friday where we got to borrow books from the library at school. I always looked for the books that had cats in them as characters.
I just had a google search, and I could be wrong but I think it is the Carbonel series by Barbara Sleigh.
"Carbonel is a children's book series by Barbara Sleigh, first published by Puffin Books from 1955 to 1978. Also published in the US by Bobbs-Merrill from 1955. It has three novels, first Carbonel: the King of the Cats and two sequels, The Kingdom of Carbonel (Puffin, 1961) and Carbonel and Calidor: Being the Further Adventures of a Royal Cat (Kestrel Books, 1978), and was based on the old British folk tale "The King of the Cats"". - wiki
I found one of the books that I adored. Its called The Cricket in Times Square by George Selden.
Update 2: It was also the Catwings series that I particularly enjoyed.