
Get some builders bags and fill them up then run them down to the local tip.
You might find a local company willing to do the removal of waste but they may charge a fair bit. You also have to check they are registered waste carriers like I am which is available online via the Environment Agency's web site.
Good shredders cost a fair bit and I can't recommend the cheaper ranges as I've not used them.
I have in the past filled a ton bag up and then used my clearing saw to cut the cuttings up which enables me to pack more in.