The majority of research council funding (MRC, BBSRC, ESRC to name a few of the major ones) distribute their funds direct to the Universities who have applied for their studentships. It is then up to the selected University to find the right candidate for the studentship. This effectively means you have no reason to approach the research council for funding, but instead approach those Universities which hold a number of studentships in the department relevant to your interests. Whether the department has a specific project in mind is another matter, but in most cases titles are sufficiently broad to tailor whatever topic to your needs and strengths whilst satisfying the research council at the same time. And whatever project you start on no decent supervisor will ever expect it remain on exactly the same track on which it started.