@annedonnelly I take care of our communal back garden.
The garden had been severely neglected for ever, at some point a laurel hedge had been planted - by the local council, I guess, because it's beyond our boundaries. This never been trimmed hedge is now a mini forest.
This year I am going to tackle it, got myself a mini chainsaw

but just enough to let some sun in.
I will get the professionals do do a proper job when my budget allows.
During lockdown I engaged a tree surgeon to get rid of some mega shrubs and to trim about 4 trees, it was almost £2000!
I did look into domestic wood shredders, but the flimsy ones are no good, plenty of reviews on Amazon, then where to keep it if you buy one?
The more substantial ones: would you be strong enough to move it/operate it? Again, where to store it?
'd really suggest a tree surgeon with a proper chipper. It will be quick, everything will be taken away. Make sure they can grind out the stumps. Tell them you won't pay until they have.
Keep the wood chips: a thick layer of cardboard, a thick layer of wood chips on top, kept my area clear of weeds for 3 years. And you can plant on the area right away.
I did had some Leylandii branches but ended-up just leaving them to rot in a wildlife wood pile
That's what I do with garden waste too thick for the compost pile.
Eventually it will compost.