My allotment was full of thistle last year when I took it over. I did not remove any of the thistles. I cut them to the ground and covered in cardboard and compost.
It is now a year later. Thistles do emerge here and there and I pull them whenever I spot them, mostly at a very small stage when they are not too prickly to pull by hand. They are appearing less and less, so I guess this approach works.
