If you can get SBK, a brushwood/stump killer where you are, drill into the stumps and large woody roots and apply SBK, or another brushwood/stumpkiller. Shouldn't affect your foundations; the stumpkiller will stop regrowth, but it will take some years for the roots to bio degrade.

Thanks Bamboo. I am just concerned that when the roots degrade a void will be created, undermining the foundations.

Using stumpkiller, as I said, means no regrowth - but the roots will take years to gradually bio degrade, so they won't leave a large gap.

Thanks again. I'll try it.