The "female singer" you refer to might be June Tabor and the track is on "Ashes and Diamonds" (check title). Yes is does run into "Flowers of the forest" but played on electric piano/synthesiser by the sound of it - which dates it I guess.

I saw Eric Bogle last summer on his UK tour. In a little village hall in a place called Rothienorman in Aberdeenshire, Scotland. He is well worth a listen and I hope he comes back this way.