Miss Marple, knowing her friend to be of sound mind and quite unimaginative, believes her. Unfortunately the authorities don't - understandably as no body is found.
She has a son, Roderick, who lives in Ceylon. She also has a daughter, Margaret, who lives in London.
During most of the events of the novel, Mrs McGillicuddy is in Ceylon. However, at the end of the novel, Miss Marple asks her to return to England, telling her that it is her duty, because someone might be killed at any moment.
Mrs McGillicuddy goes to Rutherford Hall with Miss Marple, and acting on Miss Marple's instructions, asks to go upstairs. When she comes back down, she sees the murderer from behind, and recognises him as the man on the train.
Elspeth does not appear in MGM's 1961 adaptation Murder, She Said. Here Miss Marple herself is on the 4.50 from Paddington train and witnesses the murder.
In BBC's 1987 adaptation of 4.50 from Paddington, the character is played by Mona Bruce. The portrayal is similar to the original novel except that after leaving St Mary Mead, she goes back to Scotland. Miss Marple brings her down again for the denouement.
In ITV's 2004 adaptation of 4.50 from Paddington, the portrayal of Elspeth McGillicuddy is quite close to the original novel. After reporting what she had seen, she left the investigaion to Miss Marple and went to Ceylon to see Roderick. Miss Marple asks her to fly back from Ceylon for the denouement. In this adaptation, the denouement takes place on board the same two trains. Miss Marple is with the family on one train and fakes her choking from a fishbone in order to get Quimper to give her a throat examination. Elspeth is with Inspector Campbell on the other train. She exclaims when she sees Quimper with his hands around Miss Marple's throat and identifies him as the man she had earlier seen strangling the woman. Campbell then pulls the emergency cord of his train while Miss Marple pulls the one on hers. Campbell and Elspeth cross over to the other train to arrest Quimper.
In NHK's anime adaptation 4:50 from Paddington, Elspeth McGillicuddy also plays largely the same role as in the original novel. She goes with Miss Marple to report to Constable Hearst. When Hearst has to terminate the investigation because they can't find the body, she, Miss Marple and Mabel West ride the 4.50 train from Paddington to Roxeter. They fail to come alongside another train so Elspeth thinks she has failed. However Miss Marple reassures her that this might have happened because their train was running a few minutes late. Elspeth departs St Mary Mead but in this adaptation, she is headed for the south of France. Miss Marple and Mabel then take the 4.33 from Paddington to Market Basing, the train that might have come alongside, and which they think the murderer was on. At exactly the right time and place, this train comes alongside the 4.50 from Paddington. Despite her key role in the plot and number of lines, the voice actress behind Elspeth is not credited.