Personally I'd go to A&E and say that you have accidently knocked your toe nail off. A friend of mine trapped his finger in a car door and lost his nail. He went to A&E and there wasn't a problem. Your GP may not like it as they get a bill for £78 but it is an accident and your GP would probably refer you to podiatary services anyway. Don't feel bad about using the services which are there for you.
The sad fact is you do get a better service out of A&E as they will explore all possibilities and spend as much time as necessary on your case. Your GP will give you ten mins. It is very important that you do not allow infection in and any bandages should not be sticky, the type that dirt and dust can stick to, and that the bandages are changed regularly. You must keep it clean until you can get some medical attention.