Couldn't find a Remove button.
But back to the plot - here's a note on how I resolved the issue for anyone facing similar issues in future.
My problems with the w5100 on the Due disappeared when I reinstalled the IDE (I used the nightly build as of 14 April 14 but I am pretty sure that the current beta of 1.5.6r2 would have been OK too) and moved my sketch into that hierarchy. Previously I had been using a custom location for sketches and libraries (in an attempt to be able to edit sketches under both IDE 1.0.4 and also under ERW 1.0.5 when the extra functions were of value) and clearly the compilation was pikcing up the wrong versions of libraries.
One oddity - I couldn't get output via FTDI to work on the Due's Serial1 with the w5100 connected (which had been OK on a Mega) but all was fine using Serial2.