Waugh was born, the son of a clergyman, in Settle, North Yorkshire and attended theological college in Bradford before moving to Newbury in Berkshire and then in 1866 to London.
Working as a Congregationalist minister in the slums of Greenwich, Waugh became appalled at the deprivations and cruelties suffered by children. Critical of the workhouse system, the Poor Law and other aspects of the criminal justice system as it affected children, he wrote a book (The Gaol Cradle, Who Rocks It?, 1873) urging the creation of juvenile courts and children’s prisons as a means of diverting children from a life of crime. He also served on the London School Board from 1870 to 1876.
He was also, from 1874 to 1896, editor of a religious periodical, The Sunday Magazine, in which he published several of his own hymns.
In 1884, he founded the London Society for the Prevention of Cruelty (echoing a similar initiative in Liverpool), launched at London's Mansion House on 8 July. The London body’s first chairman was veteran social reformer Earl Shaftesbury. It evolved to become the NSPCC some five years later (14 May 1889), with Waugh as its first director and Queen Victoria as its first patron.
A house in Croom’s Hill, Greenwich marks one of Waugh’s residences. He later retired, in 1905, to Westcliff in Southend, Essex, where he died three years later.