In response to Harry Pollard's question as to who first contended that demand deposits are money, I do not know enough of the history to give a definitive answer, but I do know that it was still a matter of hot debate in the 1920s when Edwin Cannan was insisting that only currency (notes and coin) should count as money, and that banks do not create it. 
Allyn Young (1976-1929), who succeeded Cannan to the Chair of political Economy at the LSE in 1927, wrote in a letter to Cannan dated June 22, 1926: "I can quite understand that you would have liked to have been followed by one of your own pupils, if that had been possible. Yet, although not a pupil of yours, I can at least put forth a claim to some measure of discipleship. Except for a few points in monetary theory (for example, I should hold that banks _do_ "create" deposits!) I think there would be very little difference between us."
Lauchlin Currie (1902-93), who was a pupil of both Edwin Cannan at the LSE (1922-25) and Allyn Young at Harvard (1925-27), followed Young in his definition of money to include demand deposits -- but also to exclude interest-bearing time deposits (contrary to Keynes and many others). Currie spelled out his reasons in _The Supply and Control of Money in the United States_ (Harvard U.P., 1934). 
Chapter II ("The Concept of Money") looks at some of its history and upholds J.S. Mills's views (while somewhat critical of Keynes's). In chapter V ("The Concept of Credit") - originally published in the JPE 1933 - he remarks that the slippery term "credit" had been "in the way of acquiring, among monetary writers [such as Hawtrey, Taussig and Young], a fairly precise connotation: means of payment represented by demand deposits. In recent years, however, and particularly in America, it has become increasingly identified with something else -- loans of all kinds, and particularly bank loans and investments."
Currie demonstrated the terrible policy mistakes that had been made as a result of confusions associated with the word "credit". He appealed for the abandonment of the term, and constructed the first ever series of "money" for the US, according to his own definition as currency plus net demand deposits (i.e., exclusive of cheques in process of collection) including US Government demand deposits. 
Roger Sandilands