From the outside, Cambridge can look a confusing place to apply to for cosmology since research in this area is conducted in three departments: DAMTP , Institute of Astronomy and Physics (Cavendish Laboratory). Students are affiliated with one of these, but there is a lot of interaction across departments facilitated by the KICC. Links to the respective Graduate Admissions pages are below:
More specific information can be found at
https://www.ast.cam.ac.uk/students/prospective-students/postgraduate
https://www.phy.cam.ac.uk/admissions/postgraduate
https://www.astro.phy.cam.ac.uk/gradresearch/gradresearchareas
https://www.maths.cam.ac.uk/postgrad/finding-damtp-supervisor#Astrophysics