"K" wrote in reply:

I know that I'll have to deal with seedlings, but am I right in thinking
that, because they're annuals, I can rake up the old stems and then
rotavate
the beds and they won't regrow from the roots?

"Control: Control measures should aim to prevent flowering and if this is
achieved before seeds are set, eradication is possible in two to three
years.

Thanks to everyone for all the advice re Himalayan Balsam. I managed to get
out before the snowfall and I raked them out and then covered the beds with
tarps. I await the lovely crop of seedlings in a month or so!