I'm in a good position to offer advice. I turn 17 on 10th May, and I've literally just got my provisional this morning. I sent off for it about 2 weeks ago roughly, probably less than that.
All you need to do is put your passport number on the form; you can send the passport if you wish, but I only put the passport number as my form of ID. They then look it up on their database and get your proof from there. Note: on the form it says "if you have a digital passport" for the option of putting your number. Don't be confused by this like I was; just put your passport number in and it'll be all right.
Even my signature went outside the little white box, and it turned out ok.