From pages 79-95 The Life of Mark Twain - The Middle Years 1871-1891:
In May 1873 Samuel L. Clemens made good on his promise to escort Olivia to England. His purpose in returning was threefold: to introduce his wife to the mother country; to research his next travel book, a project that would soon be abandoned; and to secure imperial copyright on The Gilded Age, which had just been published in the United States. Joining the three Clemenses were Livy's Elmira friend Clara Spaulding, daughter Susy's nurse Nellie Bermingham, and Sam's personal secretary Samuel Thompson. On May 15 Sam led the party of six from Elmira to New York City. They were greeted there by Mary Mason Fairbanks, who overnighted with Livy in their cabin aboard ship while Sam slept at the St. Nicholas Hotel. ...
Sam sailed with his family on the Batavia, once again under the command of John Mouland. ...
From a Letter to Paine from Clara Stanchfield in 1911:
The 1873 trip lasted only four or five months, and was spent mostly in England. My mother was in England at this time visiting an English friend. I left Mr. and Mrs. Clemens for a month or six weeks and went with my mother for a trip to the Continent. After joining Mr. and Mrs. Clemens again we went to Edinburgh and were there six weeks. It was at this time that we saw so much of Dr. John Brown who took a deep interest in the Clemens family, being especially fond of Susy. Our stay in Edinburgh was a delight owing to this lovely man’s kindness and hospitality.