Uncle Henry was a relative of Miss Marple. He was very fond of puns and flowers.
In Strange Jest, Miss Marple described Uncle Henry as an extremely shrewd and suspicious man. He thought, for example, that the servants were trying to poison him and insisted on eating nothing but boiled eggs on the grounds that one could not poison the inside of an egg. He was known to keep a lot of money in the house. He bought a large safe and made a big fuss about it and how secure it was. Eventually, some burglars broke into the safe using chemicals, only to find that it was empty. It turned out that Uncle Henry had hidden his money behind some books of sermons in the library, reasoning that no one took such books off the shelf. Miss Marple used Uncle Henry as a parallel of Uncle Mathew Stroud. Her point was, in trying to discover where he had hidden his money, one must first understand the mind of the man.
In Tape-Measure Murder, Miss Marple mentions an Uncle Henry who "was a man of unusual self-control", and was very fond of flowers, like Arthur Spenlow. This may or may not be the same Uncle Henry who was mentioned in Strange Jest.