If the obligation comes from an authority (school, government, profession etc.) , use "have to". For e.g. I have to wear school uniforms.
If the obligation is not by an authority, but you feel the obligation yourself, use "must". Because you believe the necessity of this rule, too.
For e.g. We must set out early tomorrow.
( Think about a journey. You believe that it is better to start the journey early. It �s not a rule of authority but you put it as a rule for yourself and you think it �s necessary.)
However, the rules of authority can also be used with "must".
E.g. I must wear school uniforms. ( It is a school rule but you think that it is necessary, too.)
I have to wear school uniforms.
( It is a school rule but you do not express your idea about the necessity of this rule. Ypu just mention the rule itself.)
I hope it is much clear for you. Last, I do not think that it is an issue of British English or American English.
Greetings from Turkey.
Gulsah
