In theory, the burden of proof is on them to prove that you were living there and therefore liable for Council Tax.
In practise, if you don't, it can slow things down - especially if you are awaiting something of benefit (eg- re-assessment, Council Tax Benefit, rebate etc.)
I was awaiting a rebate from my old council (an East London Borough), but they refused to issue it to me because there were arrears dating back to three years before I bought the property. They refused to issue the rebate until I proved I didn't live there.
In one of my (many) telephone conversations with them I asked "how many properties in the Borough had arrears on them?"
"We can't divulge that information" they said.
"Well, do you want me to prove I didn't live in all those f***ing places aswell?!?" I replied.