How can I remain in the UK after graduation?

My daughter Brandy is an American student about to graduate from Middlesex University in London with a degree in Music business. She has made a life for herself in London and wants to remain there long enough to obtain permanent residency. She has great references, incredible work ethic, and is musically talented (voice, songwriter). Her current job does not pay enough nor is the company large enough to sponsor her Visa. The same holds true for the internship Brandy received. Additionally the changes in UK immigration laws are making it that much more difficult for Brandy to stay. Does anyone have any ideas, suggestions, employment leads, or inside information from your own experiences that could help her out? This is a serious, legitimate post so please only serious, legitimate replies. Thank you, Mary Lawrence