You’d have to read the small print to see if next day delivery was guaranteed, almost certainly they will have a clause which excludes adverse weather because the courier companies will have the same. I think you’ll find you’ll get nowhere with legal or other threats. I’d write them an email explaining your position and that if they cannot resolve the issue they will have lost you as a customer, you may want to suggest that you’d accept a credit note as an act of goodwill on their behalf
Oh and I’ve saved a damn site more than £7 using them in the past. 🙂