Thanks for the reply.
That link goes to some complicated legal jargon, so I'll try to explain the basic principles:
In order to be able to sue someone, you normally need to establish 'negligence'. If the club had caught fire (and not because of any negligent actions by anyone connected with the club) and your jacket had been destroyed in the blaze, you'd have no right to claim any compensation from the club, because they had not been negligent. However, it appears that the most likely cause of your jacket going astray is, at least in part, the result of negligence by their staff. (i.e. even if someone deliberately tried to steal your jacket from the cloakroom, the club staff were negligent because they failed to properly check the tickets).
What the Unfair Contract Terms Act does it to invalidate any attempt by the club to say "We're not liable for what happens to your property, even if our staff are negligent". The Act isn't a piece of legislation which directly leads to court actions. Instead, it provides legal guidance to courts which are already considering cases. So, if you took the matter to the County Court, the club might say "We're not paying out. The customer should have read the sign". However, the Court would then consider whether the sign had any validity in law. Because of the Unfair Contract Terms Act, it would almost certainly rule that the sign had no effect because it sought to state that the club should not be held liable for customers' losses incurred through the negligence of its staff.
Chris