I would contact the council and ask for advice. It’s not illegal to use barbed wire but they have a duty of care with it.
If the council deem what they have done as safe then your best bet would be to install your own fence to stop your dog running into their garden.
The best bet would be to get the council to come and look, but try not to get too emotive when calling them
Just as an aside here, badgers are a hedgehogs natural predator and you may find they kill your hogs. I would not be encouraging them