What should I do about my fast track interview for a passport?

I have an interview on Thursday for fast track service to get a UK passport but I have a problem. On the form I need my parents details etc. which I do have but they were born outside the UK. (I was born in the UK) I don’t have the relevant documents to support their nationality at the time of my birth: so, what is the best course of action? Should I go to the appointment with the information and tell them that I do not have that information or should I just put that I am no longer in touch with them so cannot access any information?

If I were to put ‘unknown’ on my passport, would this mean I could not go for a fast track passport? I need this by The start of August, so I need to make sure it all goes smoothly. I know since I’m an adult they shouldn’t ask me about my parents if I do not know about them, but in that case will I need birth certificates and such?

What experiences has anyone had with fast track if you put ‘unknown’ on the form?