Many years ago I saw a British black and white movie. I saw it in the early 60's so I assume it was made in the late 50's. It was a murder mystery about a man who stabs someone and afterwards washes the blood off his hands in a small puddle of water that is straddled by a wooden fence. A young girl happens to be on the other side of the fence at the moment and sees the hands being washed and notices a distinctive ring on one of the fingers. Later on, she sees a man with the same ring on his finger and realizes he was the killer. It is very similar to the incident in “Summer Storm” with George Sanders and Linda Darnell. The distinctive thing about this movie was the theme music. It was a British nursery rhyme; “Oranges and Lemons”

Say the bells of St. Clement's “You owe me five farthings” say the bells of St. Martin's

“When will you pay me?” Say the bells of Old Bailey……

I would be much obliged if you could tell me the name of this movie.