A Ticket to Oblivion by Edward Marston

Young Imogen Burnhope and her maid Rhoda board a non-stop train to Oxford to visit her Aunt Cassandra, who waits on the platform at Oxford station where the train terminates, to greet them. Only they never arrive. All the passengers alight but the two women are nowhere to be seen. The train is searched and the coachman swears he saw them board onto first class, but they seem to have vanished into thin air. The Railway Detective must unravel the mystifying web of their disappearance before Imogen and Rhoda vanish into oblivion for good.