Some colleges only have single rooms, some only have shared, and some have both options. You should research which colleges offer single rooms. Some colleges even have En Suite single rooms if that’s what you’re looking for.
When the time comes to rank your college preferences (Durham will email you) you can put down colleges which offer single rooms as your top choices. Additionally, you’ll be able to choose your preference for a single or shared room (if your college has both) once you’ve been allocated your college.
There are, of course, a limited number of single rooms. However, if when the time comes to give your preferences you note down that you would like a single room, it’s basically guaranteed that you’ll get it. Just make sure you complete the form before the deadline!
Also, if you have a specific condition that means you need a single room, you can let Durham know and they can accommodate you accordingly.