Sunshine - you say you don't like the concept of breakfast because you don't like the thought of eating so soon after getting up.
So instead, your children go without carbs and protein from supper time (you say that is at bedtime - I am assuming 7.30pm or thereabouts), until lunchtime the following day - which is a minimum of 16.5 hours! That is really not healthy for them at all.
Eating some carbs for breakfast, and/or something with protein in it is NOT gluttony - it is normal and sensible. Restricting what your children eat for breakfast as much as you do, is not normal, honestly.
As another poster said, you have trained your children to accept this breakfast - that doesn't mean it is the right thing for them. It does sound like your issues with breakfast are affecting their diet.
There really are plenty of healthy options for breakfast - toast and peanut butter, porridge, eggs (which don't make people smell), pancakes, good quality cereals bagel with cream cheese and smoked salmon - and yes, sometimes fruit and yoghurt. Please let your children have a more varied breakfast!
Oh, and the reason so many of us are telling you that your children's breakfast is not right is not because we are feeding our children crisps and milky ways for breakfast, and no-one here thinks that is a healthy breakfast - it is because we know that children need a healthy, balanced diet, that is not only balanced over all, but is also balanced throughout the day, so that they get the food groups spread over the day - not all their protein and carbs in the last 7.5 waking hours of their day, then nothing but fruit and yoghurt for the next 16.5!!