Hi Cassava - and welcome! :)
Willowherb is pretty easy simply to pull up; there will be a reservoir of seeds in your soil - but a seed can only grow once! Pull 'em up!
Bindweed - not so easy. My bindweed comes from next door plot - covered with carpet for a couple of years :(.
I don't have a huge infestation yet, so I've been able, I think, to remove a lot of the roots - and I'm patrolling to remove every single shoot that appears! I intend to outlast it :)
Good luck - Gavin