i wouldnt call myself a sports physio just yet as im still a junior but i have a strong interest in sports. i did a sport science degree first and my physio masters after which only took 2 years so i have some sport background.I did part time work with semi professional sports teams during my studies and learnt A LOT regarding sport physio compared to at uni.

Although hospital settings may not seem relevant to sports, you will definately gain so much experience in normal outpatients departments for example. You get to see pathologies and learn treatment which you will see and treat in sport settings. Working in say an orthopaedics ward too gives you the experience to work with injuries which you may see at later stages usually if your only working ina clinic so it gives you a broader insight into the conditions.
Im currently trying to find work within hospitals full time rather than anything else as i feel that I want that experience to have a wide knowledge base.