Dredge had an interest in the various international exhibitions held both in the UK and abroad. As early as 1851, he served on the Royal Exhibition Commission. He authored several works on them, notably on the Vienna Universal Exhibition (1873) with Maw and Alexander Kennedy, as well as the Paris International Exhibition (1878). He served as British commissioner at exhibitions at Chicago (1893), Antwerp (1894), Brussels (1897), and Milan (1906). He was created a Companion of the Order of St Michael and St George for his services as Commissioner-General for Great Britain at the 1897 Brussels Exhibition. Dredge was a member of the Institution of Mechanical Engineers from 1874, the Institution of Civil Engineers from 4 February 1896, and several other engineering societies, and was appointed an honorary member of the American Society of Mechanical Engineers in 1886. Dredge was also a member of the council of the Society of Arts from 1890 until 1893. Dredge was a contributor to the Dictionary of National Biography, providing the extensive article on Henry Bessemer in 1901.