Can I make my own bread-machine flour?
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).