Daniel,
As Ashley and others have alluded to, you need to have a specific and practical skill that a U.K. employer would be hardpressed to find elsewhere to count on a job here. It's the same in the States (where a highly skilled U.S. citizen would get a job before an equally skilled foreigner would--and that only makes sense, as countries should look after their own first). The fact you have dual majors really doesn't matter, as many people get dual bachelor's degrees these days, or, at the very least, have a minor to go with their single degree.
On another note, I'm curious as to why, if you don't have a job lined up here, or a romantic interest here, you've set your sights on living here? I hope your answer isn't simply that you think the UK is "cool"--you like the music, or the accent, or the wit. What you're suggesting is a MAJOR life change. Perhaps, if you can afford it, you should spend a few months here (you can stay up to six)--give yourself enough time to get over the "honeymoon" period and get accustomed to day-to-day life--before you even worry about finding a job here/getting citizenship, etc. Just a thought.