The black plastic approach does work; but rarely quite as well as one
hopes. I'd use the heaviest I could get (old carpet is great),

Be careful with carpet, esp if you want to be organic. The carpet with the
foam backing usually contains lots of nasty, toxic materials that could /
will leach into your soil. Hessian-backed carpet is better.

Cardboard would be good, as would thick sheets of newspaper, esp if you
place the newspaper under the cardboard. Saying this, there are, AFAIK,
nasty chemical in the ink and non-white paper (eg FT)which will get into the
soil, albeit in small quantities.

The cardboard / paper mulches will degrade by themselves, avoiding future
work by you.

Best,

- h