Avoid rotavating, as this can spread and increase the number of plants. Skim off the top couple of inches of the weeds, stack the off-cuts and cover with a plastic sheet. In approximately 12 months spread this back on the garden. Then dig the land over; a good method is called "bastard trenching" or "double digging".
Nigel on plot 10 is available to rotavate your plot with his machine, at a rate of £10 per hour. Please contact him on 07895 601978.