apart from a regular spraying with a weed killer that gets to the roots, the only other solution is to clear a small area at a time by hand. I lifted all the plants i wanted from a 30x6ft border cleaned all the roots of the ground elder 'pips' and put into pots temporarily. i then dug the soil and seived it to remove the pips. took several months but i managed it in the end. if they are in between shrubs then use an old pastry brush to paint the weedkiller on the ground elder.
good luck Suffolknovice.

thanks! Haven't even heard of ground elder 'pips' before so I will look out for that. Is there any weed killer in particular I should look out for - altho I generally try to avoid as i have children & cats! Sounds like patience & digging is the answer. It is all thro the iris' that are coming up round the pond at the moment - I suppose I will have to dig the bed over up to them, saving anything I can & wait until the iris have finished flowering to do that bit? I hope the rain holds off!!!

the pip is where the leaves come from the root. as the leaves unfold there is a white bit that is not dissimilar to an orange pip. this bit remains underground over winter. Sadly digging it is the best way to do and in a rather perverse way i quite enjoyed it at the time.