No dig is not the right way to go on a weed ridden plot The clip on TV with monty don was just wrong you cannot put 6 ins of soil over a lawn or bed of weeds and grow anything.The thinking behing no dig is just all wrong on many types of soil yes if you have a light deep soil But anything like clay and its a no If you put 6 ins of nice compost on top of a hard bed of soil all the worms will live in that why would they go deeper into cold food free soil . I dig my plot evey year but with a digging hoe just turning over the top 9 ins this is done in the autum to get the frost into the soil to kill of any hibernating pests and again in the spring . some beds then get a top dressing of compost and saw dust . I now avoid horse manure like the plague even if its free ! Most vegetables will grow in 12 ins ( 30 cms ) but if you go down to 10 0r 15 cms deep then you start to restrict what will grow well, whilst each plant will require more space as the roots will spread out not go down into the mineral rich sub soil they will also need more water .
I think this is a bit oversimplified. It can work, not with spreading a bit of organic material and thinking that will eradicate every weed underneath, but by putting sheet material which will decompose over time such as cardboard, then laying organic material over this, can knock the weeds back substantially. On the community plot I am involved in, some volunteers put cardboard down on a weedy bed then piled straw on top. When I pulled back the cardboard it was nearly all clear soil underneath with just the occasional severely weakened dock which could be dug out easily. It was so clear it didn't take more than five minutes quick dig where the soil was compacted before I put some brassicas in. If I had wanted too, I could have left the cardboard down, cut holes in it an planted through in the soil underneath.
I believe another way to deal with ground that is covered in grass is to scour the top few inches containing the grass roots and lay it into clods upside down, then cover and leave it to die and rot, this provides organic material which can be put back on the soil.