If you are in England, your doctors should be able to fax (yes, they still seem to use those old fangled things) an emergency prescription to your pharmacy.
Reusing a needle is not recommended as it will blunt and you may get infection. (Yes, I know many people do reuse their needles but it should not be necessary and is definitely not recommended).
A call to your GP should be able to sort this out. I have come across some wonderful pharmacist who will do this for me. If they decline, I would go and sit in their waiting room until they provide a prescription. I might even beg and tell them you are not able to use your insulin which keeps you alive.
You may want to request two boxes of needles so you can keep one in reserve at all times in case this happens again.