It depends on your area of research. Generally in the sciences and engineering academics apply to the research councils for funding for a project and then advertise for a student. Unless you have a well formed research proposal or your own funding it is better to wait for them to advertise.
In the arts, humanities and social sciences things tend to work the other way around. Students approach academics stating their research interests. If the academic is interested he or she will assist the student in applying for research funding (with varying success).