If you are on the basal bolus regime it sounds like the background / basal insulin is not strong enough during the morning to deal with the glucose that your liver is producing. The bolus injection that you are giving to cover breakfast ( when you have it ) is in fact covering the shortfall in the basal during the morning period. So, when you don't have the bolus in the morning, your bg rises.
Depending on what your levels are at other times of the day, would mean different solutionsnto this problem. If everything else is ok at other times, then one way to counter the highs would be to give yourself some fast acting insulin at breakfast even if you don't eat. The other solution would be to increase your basal, but this may have a detrimental affect at other times of the day.
Some fasting over different periods of the day is likely to help you determine where the problems lie and assist you in making the necessary adjustments.