If you can grind out 18 inches below soil level (of the major roots) this might be enough to stop it sprouting. Alternatively, grind out the centre, then dig around and uncover the other major roots, drill into them and apply SBK to the holes, cover with something, replace the soil and leave to die.

Many thanks Bamboo and Snoopdog - the advice is much appreciated. As this is a lawn, I wanted to seed immediately. Will the SBK kill the grass seed thro 12" to 18" of soil?

SBK is something you use carefully and sparingly - it should only be applied (I use it neat, despite what it says on the bottle) directly to cuts or holes you've made in the wood, without spillage onto surrounding soil. Once you've covered it with something (to stop it evaporating too quickly and to stop contamination of soil if you have to put soil back over it) it shouldn't cause any harm to any surrounding plants. Spill half a bottle on a patch of soil, and that'd be a different story... I've certainly used it on ivy roots in areas where they're surrounded by other planting - for small roots, I always use an old flowerpot, upturned, over the bit I've treated below soil level, and then replace the soil, and nothing growing round and about has been affected in any way.

Thanks again, both. Very useful advice. Now confident to tackle the job.