Sounds like absolutely classic dawn phenomenon - mine used to sit at 4-5 all night then climb steeply from 5am until 10am, usually to 10-14 but if I had a lie in it could easily go to 18-19.
Unfortunately the only thing that properly fixed this for me was a pump - the dawn phenomenon was the reason I qualified for it. By increasing my Lantus to counteract it, I was having nocturnal hypos - so I qualified even though my HbA1c was ok.
I did find a solution whilst I was waiting for my pump- I would wake up at 4am (my cat would wake me up for food then anyway!), about an hour before the dawn problem kicked in, and take a 2 - 4 unit bolus of Novorapid. This meant I woke at 8am with sugars of 6-7. Better control but not ideal to have to wake yourself up at 4am...