Physiotherapy or sport and exercise scienceWatch
The only way you can become a physio is to study physio. If you did sports science you would then need to do a pre-reg masters in physiotherapy, so it is a long way around if you know you want to be a physio in the first place. You might need to to check on entry requirements for physio as I'm not sure your sport diploma will count for much and you might need to do A levels / an access to science course.
Other thing to consider is that universities are not interested in people who only want to do sport because a massive part of the physiotherapy course is everything except sport. Especially your placements will be mainly based in hospitals helping to rehab elderly and less able people.
A number of sports teams now employ Sports Therapists, which are similar to physios but they specifically specialise in sport injuries. There are degrees in Sports Therapy which may be more up your street if you feel that you only want to do sports stuff.