I think you should ask your consultant to send you on a carb counting course, particularly something like DAFNE might be useful but often a dietician at the hospital/clinic can show you how to carb count if DAFNE is not an option. Your diabetes nurse may also be able to show you how to carb count. If you have a book and don't understand it then you might find that your learning style is better suited to being shown rather than reading, carb counting once you know how isn't very difficult although it can be a little time consuming at first. It does make it better if you can count the carbs you're eating and inject fast acting insulin according to what you're eating.
Do you inject your Levemir once a day or twice a day? If you're injecting once a day then that might be why your consultant is asking you to increase that morning injection, he's trying to give you enough basal insulin to cover you better in the early mornings before you wake up to avoid those high readings. Some people find that injecting Levemir twice a day works better and if you're not already doing that and if your consultant can't get your waking readings down then perhaps suggest that you'd like to split the dose into a morning and night injection to see if that suits you better.
Something else you may want to try is do some blood glucose tests through the night. Sometimes a high waking reading can happen because you've had a hypo in the middle of the night and not been aware of it. This can result in a high reading when you wake up. It may just be that your Levemir is not covering you well enough through the night and into the morning but I think it's worth testing (set your alarm for maybe 11.30pm, 2am and again at 4am) just to see what's happening with your readings and rule out the waking high readings being due to a nightime hypo.