Choosing your own topic will be a lot harder but there are ways to find funding. Before approaching an academic; choose an area you want to work in, find a gap in literature and have a very rough methodology, ie can it actually be done. Those questions should be answered before you approach an academic. When you contact an academic you can then discuss the project and you should ask whether they would like to supervise you and possible funding sources. That is very rough but should get you started.
Or you could make a general approach to sports science lecturer about PhD opportunities and see what happens.