The letter was written by survivors Esther Hart and her 7-year-old daughter Eva eight hours before the ship hit an iceberg and sank in 1912.
The letter only survived because it was in the pocket of her husband’s coat which he gave her to keep warm.
Meant for her mother in Chadwell Heath, east London, the letter will go under the hammer at a Wiltshire auctioneers.
Esther Hart wrote that they were enjoying what she called the “wonderful’ journey”.
She said they were likely to arrive in New York early because of the speed the ship was doing.
Her husband Benjamin died along with more than 1,500 people in the disaster.
The letter will be auctioned at Henry Aldridge & Son of Devizes on Saturday.
Titanic memorabilia continues to be big business. A menu from the day of the disaster was sold for $129,000, while a violin played as the ship sank went for $1.5 million.
Auctioneer Andrew Aldridge said the letter was unique.
“It’s very rare because it’s a letter that’s written on board Titanic, which makes it exceptional,” he said.
“But what rises it to the absolute top of the pile is it’s the only letter known that was written on Sunday 14 April, so the day the ship hit the iceberg.
“So we can say with absolute certainty that about 12 hours after this letter was written the Titanic was at the bottom of the North Atlantic.”
The letter, embossed with the White Star Line flag, is headed “On Board RMS Titanic” and dated “Sunday afternoon”.
In it, Esther Hart describes being sick the day before and unable to eat or drink.
She said she had since recovered and had been to a church service with Eva that morning.
She wrote that Eva had sung “so nicely” to the hymn Oh God Our Help In Ages Past and they were both due to sing in a concert on board “tomorrow night”.
Remarking on the stability of the ship, which was not supposed to roll, Esther Hart wrote: “Anyhow it rolls enough for me.”
She added: “Well, the sailors say we have had a wonderful passage up to now.”
The Titanic sank on the night of Sunday April 14, 1912, on the fifth day of its maiden voyage from Southampton to New York, after striking an iceberg in the North Atlantic.
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