The roots as you may of discovered go down for feet and snap really easily. Colts Foot up here are just finishing flowering, but suppose yours have finished already hence the growth. Only thought is to either,

1 Spray it all off, then cut down dead foliage and spray any new shoots.
2 Cut it all down, spray shoots
3 Dig as much as you can out, then pray any emerging shoots.

All the above will still require digging out, but constant spraying will slowly weaken the plants and wll ensure the weedkiller gets deep down with in the roots. Only use Roundup or similar weedkiller. It may take some time as they have been made less concentrated. Any other weedkillers e.g Sodium chlortae (although now band i think) Path Clear etc will leave a residue in the soil for months and affect any plants you put in. Roundup (glyphosate) will kill only greenery that it touches.

The plant you have photographed is winter heliotrope (petasites fragranes). It is similar to butterbur but a lot smaller. It will be difficult to get rid of, though you will notice a spike of flowers which smell strongly of vanilla precede the leaves.