This was a book that I was reading as a child, in 1967 in England. Just one thing to go on (I don’t recall anything else about the book!). The (main?) child character had a cat called Shadow. I know this, because I got a cat later that year on my 8th birthday, and called him Shadow. As I say, only one short clue to go on. Sorry. It would be good to know the name and author of this book.
Lost Classics of Teen Lit: Name That Book! 
Could it be:
Magic Elizabeth
By Norma Kassirer; Joe Krush (Illustrator) first printing 1966
“Eight-year-old Sally faces an entire summer trapped in a creepy old house with no one for company but her spooky Aunt Sarah and a black cat named Shadow”
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