I had the same problem on my property last year...except w poison ivy instead of English.
We sheet mulched the plot we wanted to use after my third poison ivy outbreak.
Luckily the only thing that grew through the sheet mulch last year was a little wisteria and some blackberry weaklings, unfortunatly now I have more woodchips than places to plant. Working on learning about
lasagna gardening to potentially make more and richer soil on top of the chips.
I’m sorry I don’t have a better solution. But I feel your pain.