In 1873, Webb was serving as captain of the steamship Emerald when he read an account of the failed attempt by J. B. Johnson to swim the English Channel. He became inspired to try himself, and left his job to begin training, first at Lambeth Baths, then in the cold waters of the Thames, the English Channel and Hollingworth Lake.

In November 1986 he completed the New York City Marathon, taking four days to complete the 26 miles (42 km) race. He "ran" across America on his hands, taking three years, eight months, and six days to travel from coast to coast and raise money for Vietnam war veterans.