Apply German residence permit in UK?

Hi, I will have an academic visit to the MPII in Germany for 6 months. Which visa (Shengen visa or residence permit) I should apply? I personally think I have to apply residence permit, as the Shengen visa allows the holder to travel as a tourist for periods up to 90 days per six months. If I have to apply residence permit, I am not sure if I have to apply in London, or in Edinburgh (I am living in Durham). The website in Edinburgh doesn't mention too much on how to apply residence permit, and moreover, after booking the appointment in Edinburgh, I got a confirmation letter, saying your appointment for applying for a Shengen visa (NOT residence permit) has been successful.