Should I do a joint honours degree in English and Media Stuides, or is it best just to do English on it's own?

I am thinking of adding on media studies to degree as I am currently signed up to study English but I am extremely interested in media especially reporting and journalism. I eventually want to major in management, or Business, preferably at Oxford university, but will adding media studies onto my degree ruin my chances of getting into a notably 'picky' university. HELP