Last year I got myself a Flymo Pac a Shred garden shredder (slightly damaged plastic bin but usable) on the internet for under ? £90. Usually they are £200-£170...... I'll see if I an find the link for these.
Used it on woody twiggy bits in the late summer/autumn and just threw the shreds on the scruffy bit of my garden behind the raised veggie patch where the big weeds grow. I just trod the weeds down before I threw the shreds on.
Looked at them two days ago and all the tall weeds have gone and now there is a nice layer of composting looking stuff. So will chuck that over the veggie patch soon plus some alpaca poo from the stud up the road.
As you can see, I make it up as I go along

Gen in NBL where it is a balmy 4.5C at 5am !