Usually ring the uni. Were you below entry requirements or did you have a bad personal statement because that can make things tricky? If it was just not providing a reference then ring and say "I'm really sorry I don't have a reference to give you, but X, Y and Z happened and if I can get you the reference by [insert realistic date] will that be enough for you to reconsider?" If the problem is that no reference is coming full stop, then switching unis is probably a good idea, but you'd have to call up before applying and saying "I have no reference is that okay?"