Deciding on a research topic is a crucial part of applying to study for an MPhil or PhD. Your topic must sustain your passion throughout your degree and be innovative and novel.

If you apply for a funded studentship, you will either have the freedom to put forward a project within a broad subject area or will apply to study a pre-defined project, depending on the funding opportunity.
If you are funding your own studies, or have secured funding which does not prescribe the project you will pursue, you will need to identify and approach a supervisor.