The queen, who became Britain’s longest serving monarch in September after more than 63 years, also conducted 35 engagements abroad, having paid state visits to Germany and Malta.
Last year she carried out a total of 393 engagements.
Her husband Prince Philip, the Duke of Edinburgh, carried out 250 engagements in total last year, despite turning 94.
Their eldest son Prince Charles, 67, the heir to the throne, undertook 527 engagements, including 147 abroad.
The engagements include official visits, opening ceremonies, sports, concerts and charity events; receptions, lunches, dinners and banquets; investitures, meetings and audiences.
Charles’s eldest son Prince William, 33, carried out 87 engagements in Britain and 35 overseas. William’s day job is as an air ambulance helicopter co-pilot.
William’s wife Kate, who gave birth to Princess Charlotte in May, carried out 62 engagements, all in Britain.
William’s brother Prince Harry, 31, who ended 10 years of army service in June, carried out 49 engagements in Britain and 59 abroad.
Queen Elizabeth’s only daughter Princess Anne, 65, racked up the most engagements at 544, although the list should not be seen as a league table of the 15 royals tracked, said its compiler Tim O’Donovan.
He has tallied the figures for the paper every year since 1979, based on engagements listed in the daily Court Circular — the official record of royal engagements.
“Except for Christmas Day and Easter Day, the Queen never has a day off from the official red boxes which pursue her everywhere,” he told The Times.