I planted an area of the polytunnel with spring onions and the weeds, mainly chickweed, took over so I decided to transplant the spring onions, what remained of them, to a raised bed. Rather than dig over the chickweedy bed I covered it with a couple of sheets of cardboard and left it for a couple of weeks. Today I removed the cardboard and underneath all traces of chickweed and spring onions were gone. all the area needed was a light hoeing to loosen the soil and a good watering. Not a weed in sight! It should be ready for planting tomorrow.
I cleared another area which was dry and full of small stones. I gave it a very thorough watering and added a thick layer of well rotted compost. Then I covered it with a good layer of cardboard and plonked four grow bags on it. I expect that in four weeks or so it will be in perfect condition for planting.
So - winning the war on weeds one battle at a time. In the polytunnel anyway. The War Against Convolvulous in the perennial beds may prove a much tougher match.