The Oxford Martin School is one of the few academic institutions that focuses on emerging technologies. For instance, see their "Big Questions" page. One of the notable groups under the Oxford Martin banner is the Future of Humanity Institute .
From the description on their about page:
The Oxford Martin School is a unique, interdisciplinary research community of over 300 scholars working to address the most pressing global challenges and opportunities of the 21st century. From the governance of geoengineering and the possibilities of quantum physics, to the future of food and the implications of our ageing population, we support over 30 individual research teams from across the University of Oxford to consider some of the biggest questions that concern our future.