The 1,309 passengers will hear 10 lectures and participate in two memorial services -- one marking the place where the Titanic struck an iceberg before it went down in the North Atlantic east of New Foundland, Canada, The Independent said.
Tickets for the 12-night memorial cruise, which began Sunday, cost as much as $9,500 and had been sold out for months.
Jacki Free, an IT consultant from Bolton, who was traveling with her husband, three children and relatives, defended wearing her "Kate Winslet arrival dress" worn by the lead actress in the blockbuster "Titanic" movie 15 years ago.
"If I came wearing 2012 attire people might say I'm being disrespectful," Free told The Independent. "This is a Titanic memorial cruise so it is about putting yourself in that time and era. It's about respecting those we have left behind."
British travel company Miles Morgan, which orchestrated the cruise, promised an "authentic" and "sympathetic" flavor of Titanic life, including food from the original menus of the White Star Line ship, and a Belgian band playing the same selection of music as in 1912.
Several relatives of Titanic victims and survivors are among the Balmoral passengers, including Philip Littlejohn, grandson of Alexander Littlejohn, a steward in Titanic's first-class section who survived by rowing one of the ship's16 lifeboats.