Shortly after his birth, the Allison family travelled to England for business purposes, and it was there where young Trevor was baptised.
He travelled on the Titanic with his father Hudson Allison, his mother Bess Allison, and sister Loraine. He was also accompanied by a nurse Alice Cleaver, a cook Amelia Mary Brown, a maid Sarah Daniels, and a butler, George Swane. They boarded the ship in Southampton. Hudson and Bess occupied cabin C-22, Sarah and Loraine occupied C-24, and Alice and Trevor occupied C-26. Two second class cabins were also booked for George and Amelia.
After the ship struck the iceberg, George saw Alice, Amelia, and Trevor safely into Lifeboat 11, which left the ship at around 1:45 AM. Sarah had also left in one of the earlier boats. She had gone up on deck to investigate the commotion and was hurriedly placed in a boat by a steward who promised to inform the Allisons of her whereabouts. Varying stories claim that Alice panicked and grabbed Trevor, without informing Bess that she was leaving, and that Bess refused to leave the ship without him, though it is possible that the entire group went up on deck together and that Alice and Trevor were lost in the crowd.
Hudson, Bess, Loraine, and George were all lost in the sinking. Whether or not George found his employers and informed them that Trevor was safely off the ship is unknown, but if he did, it is likely the information came too late for any of them to leave the ship. Of the Allison family, only Trevor survived.
Alice and Trevor were met in New York City by Hudson's brother, George, who, along with his wife, Lillian, took custody of the now orphaned Trevor. The media initially treated Alice as a hero, but later accusations emerged that she had killed her illegitimate child in 1909. Eventually these claims were shown to be false: the real murderer was one Alice Mary Cleaver, who was already in prison at the time.
Trevor died on 7 August 1929 at the age of 18 in Maine, USA of ptomaine poisoning and was buried beside his father in Chesterville, Ontario.