I'm assuming the company hasn't volunteered to come out and assess the problem before dismissing it? That won't work in their favour.
Will the local builder give you a report to back up the claim? Sounds like a slam dunk to me but the CC company might need more persuading. Gather as much evidence as you can.
If CCC fails then small claims court would the route I'd follow, and some honest reviews of the company all over Twitter and review websites.