Uncle Jack is a relative of Jane Marple. She referred to him the course of speaking with Professor Wanstead during her last chronological murder mystery, Nemesis. Uncle Jack had a wife, who claimed that she could smell when someone was lying.
Jack Marple?[]
Since Miss Marple is a spinster it is quite likely that Uncle Jack is Jack (or most probably James) Marple. In the same adventure and conversation Miss Marple refers to an unnamed Aunt who spoke to Uncle Jack. This unnamed Aunt may or may not have been Uncle Jack's wife, or sister.