Beesley was educated at Derby School, where he was a scholar, and afterwards at Caius College, Cambridge, again as a scholar. He took a First Class degree in the Natural Science tripos in 1903.

Beginning as a schoolmaster at Wirksworth Grammar School, he moved to Dulwich College, where he was a science master. In 1957 he was still teaching as Principal of the Northwood School of Coaching, Northwood, Middlesex.

One of the survivors of the sinking of the Titanic in April 1912, Beesley wrote a successful book about his experience, The Loss of the SS Titanic (June, 1912), published just nine weeks after the disaster. He saw two second class women who tried to get on a lifeboat, who were told to go back to their own deck, that their lifeboats were waiting there.

During the filming of A Night to Remember (1958), Beesley famously gatecrashed the set during the sinking scene, hoping to ‘go down with the ship’ a second time. But he was spotted by the director, Roy Ward Baker, who vetoed this unscheduled appearance, due to actors' union rules.