If it is going to be your first year at UCL, the university will provide you with an accommodation in one of UCL’s own Halls of Residence (catered) or Student Houses (self-catered). They offer a variety of options when it comes to sharing facilities with other people, and you will be able to ask for an ensuite room with shared kitchen. You can get further information on eligibility, allocation of places and the application process here: www.ucl.ac.uk.
However, if you don’t find anything that suits your taste, you can rent a room in Private Halls, meaning that they are run by independent organisations and not by UCL. These tend to be more expensive, and they will have students from many different London universities living in them. There is a page on UCL website dedicated to private halls as well: http://www.ucl.ac.uk/prospective-students/accommodation/residences/private-providers. Private Halls listed on UCL website have a number of rooms which they leave solely for UCL students, and in order to get such rooms, you will still need to use UCL application services. There are also Intercollegiate Halls, run by the University of London: http://www.ucl.ac.uk/prospective-students/accommodation/residences/intercollegiate-halls.
During my first year at UCL, I lived in Frances Gardner House (UCL Student House, self-catered), in an ensuite room with a shared kitchen. The quality of facilities was great and it was a 20 min walk from the main campus. I really, really liked this place. And I could see St Pauls from my kitchen window!
Feel free to contact UCL Student Accommodation inquiries team:http://www.ucl.ac.uk/prospective-students/accommodation/contact-us, they can help you with an application process and answer all of your questions, even if they are not about UCL halls.