The BBC lists strong white flour as simply flour made from hard white wheat, which tends to have a higher gluten content.
By mixing all purpose flour (German: 550, French: 55) with the package recommended amount of vital wheat gluten or by using bread flour you should be able to make bread in your machine just fine. I usually use either AP flour or a mixture of AP and whole wheat (German: 1600, French: 150), or even all whole wheat (although with all wheat I find adding gluten is extremely helpful for getting a well-risen loaf).
You can also buy other types of high gluten flour, either with that label or listed as bread flour.
If you live in a part of the world with "0" and "00" flour, the protein content of "00" flour is similar to that of all purpose flour, but the grind of all purpose flour will be more coarse. "Panifiable" 00 flour has the gluten content of bread flour (source).
As eggs are a very versatile ingredient: when substituting, it is important to determine whether the eggs are being used as a leavening agent or binder (or both). In recipes where the egg is used primarily as a leavening agent, I have used a mixture of baking powder (not soda), water, and vegetable oil in a 2:3:3 ratio, though you may want to experiment with the proportions depending upon your recipe. You may also need to vary the amount of other liquid in the recipe.
Where the egg is used primarily as a binder, you could use banana, applesauce, or gelatin, depending upon the recipe (obviously, you'll probably want to avoid the fruits in a savory recipe). I've used, and been thoroughly disappointed with, the available commercial "egg replacers" and don't recommend them for any purpose. I've heard of using flax, but have no personal experience with it.
However: as the father of (and resident chef for) a young child with egg and milk allergy, it is my experience that successfully substituting for eggs is very difficult. For breads in particular, I don't even bother with recipes that call for eggs or milk, and favor those that use the basic 3 (4): flour, water, yeast (salt).
Best Answer
In my experience, it doesn't really save money, but it's still worth it because it's fresh and better than store-bought at the same price.
For me, 1kg of all purpose flour yields 1.6kg of bread (as two loaves). Each 13x4x4" (Pullman) loaf weighs about 800 grams after cooling and yields between 24-30 slices depending on thickness. The cost per loaf is under $1.00, and includes all ingredients, tax, and electric for mixing/baking/slicing.
I've made a few hundred loaves based on variations of this formula:
To be clear, I no longer use a bread machine. My answer focused more on how much bread can be made with 1kg flour. The Pullman loaf pan was $25, and the electric knife was $20. So for 300 loaves, that adds 15 cents per loaf. The mixer and oven are used for other things besides bread, so I don't really consider them in the overall cost per loaf.