How likely is it for an international student to secure graduate funding for a subject like Psychology? I am international student who will be commencing an undergraduate degree in Psychology at a top-ranking university in the UK. I know it's a little bit early in my "academic" career, but I have been aspiring to become an academic for some time and due to personal circumstances, I have come to a crossroads where I have to decide whether this dream is worth pursuing, or if I should give this dream up permanently. One of my main concerns is finances, as due to the steep cost of my undergraduate degree, I will most likely be unable to continue onto graduate studies without funding. 

It is my understanding that graduate funding for non-British and non-European students in the UK is rare. What is the profile of an international student who secures funding (particularly in Psychology or Neuroscience) in the UK, and is there anything I can do now or in the years ahead to improve my chances? At the same time, how likely can an international student with only a 3-year British undergraduate degree secure funding for graduate studies in other countries, such as the US, and again, is there anything I can do to improve my chances?
My former UK Psychology department ran a neuroscience program. At the PhD level we had funding from outside grants, school funding, and university funding. Typically only the school and university funding could be used for international students. Technically, this means maybe 1/3 of the available funding could go to international students, but the school funding was almost always ear marked for special cases (i.e., a new faculty member or a supplement for getting a grant, or a reward for doing extra teaching). More typically only about 10% of our funded PhD students were international.