[woodburner]

If you can get a load of well rotted manure that is also free from pyralid, you can grow no-dig potatoes.
Put down a load of cardboard, cover with a couple of inches of manure, (more if you have loads of it, ) plant the spuds into the manure. Use straw to earth up until as high as you would normally leave, then cover with grass clippings or soil from elsewhere on the plot to exclude light. Some couch grass will make it through, but is easily dealt with.

Brassicas can be planted through weed suppressing mulch or cardboard, also cucurbits (Pumpkins, courgettes cucumbers etc. ) and fruit bushes.