DAAD definitely supports german citizens to pursue a PhD, also abroad. I guess DAAD-funding is less difficult to get.
Institutions like SdW, Konrad Adenauer, Cusanus and so on offer studentships but you should participate in activities, will be difficult when in UK. My Brother for instance has to participate once a month in activities.
If you can read german have a look at this link: http://www.e-fellows.net/show/detail.php/5789, very useful! You can look for scholarships in Europe.