Is there any way to get my old village which hasn't used Game Center onto a new iPhone?
Solution 1:
Try to delete COC on your new phone. Then delete the saved date in your Game Center. Connect COC from your old phone to Game Center. Then reinstall COC on your new phone and connect to Game Center.
You can also make a new Game Center account. Connect it to your old phone and save savegame. Then log in on your new device with your new Game Center account and restore the old savegame.