Even further to this, I found the problem:
First I tried the Cura slicer in place of Slic3r and it gave me sensible filament requirements in "Printing Statistics" so it appeared that the problem was Slic3r related. After much digging, poking and drilling-down in Slic3r I finally found a parameter "G-Code Flavour" which is set to "No Extrusion" by default and needed to be set to "Repetier" (in this instance).
(Since, with this default, Slic3r wouldn't actually do anything useful in any situation, I'm surprised that it doesn't draw attention to this parameter and recommend that it be set to something workable on initial installation.)