I have cut down a large ivy, and there is about half a tonne at least of
leaves
branches and thick trunk.

Getting rid of it is a problem, Which do you consider the best way:-

Hiring a shredder and composting it or pay for it to be taken away

I have composted small amounts of clippings in the past with the other
compostable material, but I don't whether such a large amount of ivy
composted by itself would prove toxic to the soil.

Any ideas????/