This was mentioned in Underground London and while Gutenberg didn't have a copy, it is available online here at Nostalgia League. Although the story doesn't seem long at all at that link, this book is supposedly 30 pages. It's also one of a series of mysteries that Orczy wrote with the character of "The Old Man in the Corner" - you can read six more of them here on the same website: The Nostalgia League Library, The Baroness Orczy Solarium. (I did find that Amazon has the collected stories on kindle for free here, but still couldn't find it on Gutenberg - weird.)

Orczy is very much a writer of her time (this book is dated about 1909), and big on the melodrama. So when one character is sitting in a coffee shop and the next minute the Old Man is regaling her with the mystery - well, you have to just go with it.

From the story - a bit of commentary on the underground:

"...In these days of tubes and motor traction of all kinds, the old-fashioned 'best, cheapest, and quickest route to City and West End' is often deserted, and the good old Metropolitan Railway carriages cannot at any time be said to be overcrowded. Anyway, when that particular train steamed into Aldgate at about 4 p.m. on March 18th last, the first-class carriages were all but empty.

"The guard marched up and down the platform looking into all the carriages to see if anyone had left a halfpenny evening paper behind for him, and opening the door of one of the first-class compartments, he noticed a lady sitting in the further corner, with her head turned away towards the window, evidently oblivious of the fact that on this line Aldgate is the terminal station..."

The female character is a journalist, and Orczy has another book with a female detective who works with the police - so in that you do have to see Orczy as modern, and noteworthy. But as the wikipedia page on the Old Man says these are "sensational" stories, meant to jump in and get you into the action and not really big on character or backstory. ( )