What you are experiencing is something commonly known as the dawn phenomenon, which is not fully understood yet. For some reason, most of us will see our blood sugars rise of their own accord for a couple of hours after we wake up. It's thought that our bodies give us some adrenaline and glucose to get us up and moving when we first wake. I find that I suffer from this as well. There are a number of ways of combatting the rise though. You could give yourself a small dose of short acting insulin when you first get up (start with 1 unit, making sure to test your blood sugars a lot while you experiment).
For the past couple of months, I have been on a newer basal insulin called Tresiba. It has drastically reduced my symptoms of dawn phenomenon. It is available on the NHS, but it is not prescribed as readily as Lantus or Levemir. This is because it's much more expensive. if you find that you are having a lot of problems controlling your blood sugars though, then your healthcare team may be willing to prescribe it for a trial period, to see how you get on with it.
Some people find that they can achieve more stable blood sugars by splitting their basal dose into two injections, 12 hours apart. Obviously they would take half the amount at each injection. Dr Richard Bernstein actually splits his basal dose into three. He gives one dose before bed, and then another dose halfway through the night, to counter the dawn phenomenon. He then gives his last dose in the morning. From what I have heard, split dosing is only recommended with Levemir. I'm not sure why it's not suggested with Lantus. Some people might do split dose Lantus as well and swear by the results, but I'm afraid I don't know what the effects of this would be.
If you make any changes to your regime, make sure to up the amount that you test your blood sugars. Hopefully this will minimise the risk of an unexpected hypo/high, and allow you to measure the results of your changes.
