Don't fret - I think this is probably simply due to what's known as liver dump, or Dawn Phenomenon. This is when your liver "thinks" you've gone into starvation mode and your BGs are dropping too low, so it helpfully "dumps" stored glucose into your bloodstream to even things out. The longer you leave it, or the more things you do before having some food, the higher the readings can get.
Some members find that a small high-protein snack just before bed (such as a small piece of cheese or a few nuts), and a cup of coffee with cream upon waking, can act as preventative measures. Most members also take FBG readings as soon as possible upon waking, before starting the activities of the day such as showering, etc.
Give it a whirl and let us know how you get on!