This google search seems to be a mine of information.
i took over a very neglected allotment 4 yrs ago. It was also the worst plot on the site. clay,shallow soil, loads of stones and thick in rubbish and weeds; but the only one available so I took it on.
I cleared as much rubbish (old bits of plastic, carpets, wood, broken tools and even soem metal and glass!) and stamped or cut as many weeds as possible.
I then covered almost the entire plot in thick cardboard - old packing boxes which you can ofter get on Feecycle. I then began to work in a systematic way to clear an area at a time having first drawn a plan of what would go where.
I took over mine in early Autumn and so was able to clear the first patch for onions, shalots & garlic. Next the perenial fruit, strawberry bed, Raspberry canes etc. and rhubarb.
All this time the weeds were dying under the cardboard and enriching the soil. Until I was at the stage when I dug straight through the rooting carboard and dug out the worst pernicious weeds and burnt them.
As the soil was cleared through to the spring i replaced some of the card board having first scattered dried chicken manure and coverd with well rotted farmyard manure or soil. I also planted loads of potatoes to help break it all up.
I could then plant through carboard for many of my plants but particularly , courgetes, beens, peas, sweetcorn. This cut the back break of digging and most of my plot became a 'no dig'. year 2 were bumper years for the crops and i would do exactly the same again.
Organically - Cut all the top growth with a flame or strimmer. Then cover the whole thing in black plastic, carpet etc etc leaving a small patch so you can start digging and seeing whats in the soil and removing the roots. When you've got through the first patch of land, pull back a bit more of the plastic and start digging and so on so....
Not organically - Blast the whole lot on a still day with weed-killer and let it die-back, once again covering the lot with black plastic and repeat as above.
Trust me, I've turned over a disused allotment, all 40ft by 100ft of it, by myself, and with 2 toddlers, took me a few years but I couldn't have done it any other way. Remember black plastic/builders sheeting is reuseable and has many uses for the future.