The letter was written by survivors Esther Hart and her seven-year-old daughter Eva, hours before the ship hit an iceberg in the Atlantic Ocean on April 14 on its maiden voyage from Southampton to New York.
The letter survived as it was in the pocket of Hart's husband's coat which he gave her to keep warm, the 'BBC News' reported.
In the letter meant for her mother in east London, Hart wrote that they were enjoying what she called the "wonderful' journey".
The letter, which was auctioned at Henry Aldridge & Son of Devizes on Saturday, fetched 119,000 pounds, which the auctioneers said was a new world record for a Titanic letter.
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"It's very rare because it's a letter that's written on board Titanic, which makes it exceptional," said auctioneer Andrew Aldridge.
"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," said Aldridge.
The letter, embossed with the White Star Line flag, is headed "On Board RMS Titanic" and dated "Sunday afternoon".
Writing about the stability of the ship, which was not supposed to roll, Hart mentioned in the letter: "Anyhow it rolls enough for me, I shall never forget it."
"Well, the sailors say we have had a wonderful passage up to now. There has been no tempest, but God knows what it must be when there is one," she wrote.