You don't happen to live near me do you? We seem to have a particularly bad problem round here. That (and couch grass) is the bain of my life in the garden. I've found it responds to glyphosate in the short term, but, as you say, the roots go down a fair way and it always seems to regenerate. I think digging is the only solution; my neighbour said they had a bad problem with it, and he just kept digging away at it until it was no more. The problem with digging (well, one of them) is that if it's growing around other plants it's much trickier to get at the roots, without damaging the plants you do want to keep.
What I have used is Path Clear on the drive for general weeds, of which there were a couple of bind weeds growing. That was 3 months back and it hasn't come back yet. The problem with that is that you're not supposed to use it where you actually want to grow stuff: it recommends an area watered with PathClear to stay plant free for 6 months or more, which on an allotment may not be practical. Still, you could give it a go a bit at a time, reducing your growing space a little, but testing it out, and, if it works, gradually working across the larger area. Might try that myself actually!