Well toast and cereals are only two of the things seen as breakfast foods in the uk, there is plenty more, eggs, sausages, bacon, porriage (but i guess this might come under cereals) you don't have to eat cereal and toast.
All that said, breakfast foods around the world are seen as different things
In europe, hot chocolate is seen as a breakfast drink rather than the bedtime one its seen as in the UK,
In america a breakfast might be buscits and gravy (scones and milk sauce) or pancakes and bacon and syrup/blueburries
In india it might be Indian tofu scramble, lentils, veggie sausage and banana pepper toast with rosemary roasted potatoes.
In japan it might Tofu with fish and rice soaked in soy sauce.
In turkey it might be few varieties of cheese, butter, olives, eggs, tomatoes, cucumbers, jam, honey, and spicy meat.
In germany it might Wursts, local cheeses, and freshly baked bread, all washed back with a strong coffee
Basically eat what you like for breakfast, all food is breakfast food somewhere. If you don't like toast and cereals you really don't have to eat them.
You seem to have quite a narrow view of what your allowed to eat at breakfast