Best thing to use is thick loads of very wet old newspaper. Soak the
newspaper overnight in the water - then place it onto the garden beds and
cover it with mulch or top soil. If you expose it or put too little paper,
it won't do the job.

Don't use plastic- they cause the clay in my soil to harden and also killed
all the worms in the garden. That was the state of it when I first got hold
of the place. The previous owner had laid down thick black plastic onto the
garden- then placed top soil onto it. Somehow it caused the death of all the
worms in the garden. I couldn't find any (earthworms or compost worm types)
despite digging around for six months.

After I removed the plastic and placed in earthworms + compost worms I found
elsewhere, the garden is doing ok.