The previous holder of the title, Tomoji Tanabe, died in his sleep in southern Japan earlier Friday at the age of 113.
Allingham is one of only two surviving World War I veterans in Britain and celebrated his 113th birthday June 6. He has been Britain's oldest man since January 2007.
Craig Glenday, editor-in-chief of Guinness World Records, said the last Englishman to hold the title of world's oldest man was Frederick Butterfield, who died in March 1974 at the age of 110.
Allingham joined the Royal Naval Air Service - precursor to the Royal Air Force - in 1915, and a year later took part in the Battle of Jutland, the war's largest naval battle. During World War II he worked on measures to counter magnetic mines.
Allingham joined activities involving other war veterans after he met Dennis Goodwin, an independent inspector for residential care homes who organized trips for veterans who wanted to return to the continent where they had fought.
Goodwin encouraged Allingham to share his experiences. He soon became one of the nation's most outspoken veterans and has long encouraged everyone to remember the sacrifices of those who died.
He co-wrote an autobiography with Goodwin, "Kitchener's Last Volunteer," - a reference to Britain's war secretary who rallied men to the cause - and was made an Officer of France's Legion of Honor.
He and his late wife, Dorothy, had two children. He has five grandchildren, 12 great-grandchildren, 14 great-great grandchildren and one great-great-great grandchild.