Formed company + visa refusal

I was refused for visa, alas. The question is: can the company continue to operate in the UK while the director (me) is permanently living in another country (it is possible to control it remotely, so it is not a big deal). And also, can I legally work for this company (as a director and in my primary functions) being abroad? Clearly, for all the profit I make I have to pay taxes in the UK and fill all the paperwork, but the question is really can I legally state that I am self-employed in the UK?

I have addressed this question to lawyers, will see what they say... In the meantime, if anyone has any thoughts, very welcome to share them.