As in the Second World War, Lloyds of London compiled lists of ships reported lost, and these were published in 1990 as Lloyds War Losses - The First World War.

However, I have not checked them all, most of the figures are different to those in Salter - for example:
August 1914 - Salter shows 64,752 tons lost, 46,603 tons of that being British flagged - but Lloyds has 67,228 tons, with 44,709 tons of British flagged