Who decides whether or not goods supplied are faulty?

[RobinOakapple]

Let's suppose a firm supplies goods to a private customer, by mail order. Under the current legislation AIUI, the buyer can return the goods for a refund, within time limits, but has to pay the return carriage costs unless the goods are faulty. The customer says the goods are faulty but the supplier says they are not.

How is this situation to be resolved?

[RobinOakapple]

I'm guessing around £25