Hi and welcome to the forums.
What you might be seeing is a fairly common thing called (usually) dawn phenomenon. What typically happens for me is that my BG will fall quite low around 3-5 am (4 am this morning) and I'll have very vivid dreams/nightmares and heavy sweating. After that my BG will slowly and steadily climb. This happens because our livers make glucose and add it to the system when it seems to be needed. Waking up in the morning appears for a lot of people to be one of those times. 7.2mmol/l isn't particularly high and certainly not "a spike".
I've found that this rise will go on for at least eight hours if you leave it alone. However, eating something seems to reassure my liver and it will scale back glucose production. The "something" can (in my case anyway) be as little as three almonds.
It happens to non-diabetics as well, so it looks like a normal and natural thing.