Pulling and uprooting is definetnly the most effective method, like ragwort you must make sure you have all the roots with you. Another mehtod is strimming or cutting but the stem must be completely severed below the lowest node or joint.
Himalayan balsam is an invasive species and it is an offence to plant or cause growth of the plant so just be carefull with the seeds which are active untill late Novemember and they can reroot if disturbed during pulling/strimming ect and cause regrowth. Technically wonce uprooted they should also be disposed of to tips which are licensed to accept waste containing invasive species, but thats getting very technical now.
Thanks Flojo. It's a nightmare - my fields are next to a river bank and the guy that actually owns the river bank just won't do anything about it! Hence I can see I'll have this problem every year (only been at this place for 12 months).
We have the same problem, another riverbank issue. I am considering resorting to the method my father used - child labour & payment per bucket/wheelbarrow of plants. Used to be 10p a bucket of seedlings.