I proofread a lot of legal documents coming from our Amsterdam office and they use both. The style guide in my company recommends that we just make it consistent. That said, lower case is more common and, it would seem, more logical - we don't usually write The United Kingdom, The United States, The People's Republic of China, etc. Indeed we tend to put the 'the' into initial lower case when a proper noun begins with 'the' except where it's in a heading. Take, for example, the newspaper I read: it is 'The Guardian' in the small-print header at the top of each page but 'the Guardian' when it appears in articles within the newspaper.
Student or Learner