My new (overgrown) allotment. HELP!

[Feral007]

i can still recommend cardboard. We laid it on top of grass and weeds. Then put homemade compost and mulch over the top. That part of the garden is still the best soil to grow in.
Son just made some waffle beds next to, and through the previous bed. He dug a shallow spade of grass and soil, and turned it upside down on the grass next to it. Then we're filling in the waffle hollows with mulch and a handful of compost when we plant seed/seedlings, and mulching more when it drops. We're doing this as we have a very dry summer and need to hold any water that arrives, and slow it's trip down the slope of our land.
Looking good so far.

But like I said, the ground that was cardboarded and compost/mulched is still growing the quickest healthiest plants. Instead of taking out the weeds, you are using them. Let them breakdown and put back into the soil what they took out. We also put the plants that the produce comes off, back onto the soil. So the corn/bean stalks and pumpkin vines etc. Use what you've got instead of throwing it away and buying in things to fertilise and condition the soil.

[Two_Sheds]

Let them breakdown and put back into the soil what they took out. We also put the plants that the produce comes off, back onto the soil. ..corn/bean stalks and pumpkin vines etc. Use what you've got instead of throwing it away and buying in things to fertilise and condition the soil.

I couldn't have said it better myself.

[Raybon]

I suppose it depends what kind of weeds you have ....digging mare's tail back in (and possibly chopping into smaller pieces, each one viable,) is maybe not a good idea.

If you dig everything out it's not lost, if you pile up the clumps upside down, removing the baddies, and allow to rot down - it can then be reintroduced to the soil as valuable compost.
Hard work, but so worth it!