Dig them out is the best solution.

Exactly. You haven't really got an option if you want them removed. Even dead they'll need digging out. They haven't got a huge root system.

Not easy when its next door coming under the concrete block at the base of the fence! Think we'll try Roundup on new growth. Thanks anyway.

I suspect you will still need to dig out. This is also a good opportunity for your son to teach his children not to eat anything growing in the garden! There are a huge number of plants which are toxic.