+1 to Charlotte's method...
...but, given the wider implications of nuclear devastation, I'd try a combination of...
1. stems with leaves tied together in a clear plastic bag (reasonably substantial) containing glyphosate... Not too much glyphosate, because sometimes the leaves are simply chemically burnt and don't seem to then take up optimal levels.
edit. After a few days of glyphosate treatment you could try & introduce some Verdone*, as a double hit. Glyphosate first, to allow good growing conditions & normal plant metabolism to carry Gly. to the roots), verdone - with synthetic auxins to stimulate over growth & plant death...
*
Verdone Extra 800 Ml Ready To Use Lawn Weedkiller: Amazon.co.uk: Garden & OutdoorsAnd,
2. continued physical removal of plants and as much root as possible; because in the end glyphosate just doesn't appear to be fully effective.
A couple of years ago I managed to get rid* of uber weed - ground elder from the front of house border, by virtually sifting the soil, removing any root particles, getting rid of clumps of plants harboring the GE (in bags to the local tip), removing a section of lawn against this border, removing any GE plants that did reappear/applying glyphosate...
* touches some wood...
On another note, beware of accepting pots of plants from other peoples gardens. At our last house I managed to get an 'infestation' of lesser celandine from a pot of perennials from my parents...