In the short story The Market Basing Mystery, Mr Parker was a man who visited local resident Walter Protheroe at "Leigh House" some three days before his death. Although Parker and his wife stayed over at the house, Miss Clegg, the housekeeper told the police that it appeared that they had asked themselves to stay. They had turned up unexpectedly and Protheroe had not seemed pleased to see them.
After Protheroe was found dead, Inspector Japp questioned Parker but found him full of bluster and abuse. He also lied about a piece of cufflink being his although his wife had confirmed it. Parker was later arrested for the murder of Protheroe when additional facts emerged at the inquest pointing to the likelihood that Parker was blackmailing Protheroe. Poirot would however discover that the nature of the crime was somewhat different.
Hastings described Parker as a "somewhat flashily dressed man with a shifty, unpleasant face." He was someone to whom he had taken an immediate dislike to.