Cardboard and lots of it then six inches of straw(not free unless you konw a local farmer), amazingly this will suppress even bindweed.....though not completely :( I've got some amazing roots under this from last year! This is in the fruit bush area which has a lovely mix of bindweed, couch grass, hogweed and feral autumn bliss ::)
Wood chip would work too and a local tree surgeon will give you a load for free but it will be fresh. Don't put it directly on any soil you want to grow on this year but it will be great mulch by next year.