How can an American citizen find a job in London?

I am finishing up at master’s degree in the US, and looking to pursue opportunities abroad. I would love to spend some time working in London, but I know that it is difficult for Americans to obtain UK work visas. Does anyone have recommendations about the best way to find a job with an employer that will sponsor me? My degree will be in public policy and management, so I’m most interested in entry-level research or analyst positions or a job at a nonprofit.