Cosmology covers a broad range of topics, from observations and numerical simulations of large scale structure to quantum field theory calculations of particle physics processes in the early Universe. At different institutions cosmology research takes place within different, and sometime multiple, groups. Here is a, hopefully fairly complete, list of research groups in the UK which contain people working on Cosmology. The links point to a list of specific PhD projects where available. Let me know if you spot any errors or omissions.
• Birmingham: Astrophysics
• Bristol: Astrophysics
• Cambride: Astrophysics (Physics), Institute for Astronomy, DAMTP (Maths)
• Cardiff: Astrophysics
• Durham: Astronomy, Institute for Particle Physics Phenomenology, Particle Theory
• Edinburgh: Institute for Astronomy, Particle Physics Theory
• Glasgow: Astronomy
• Hertfordshire: Astrophysics
• Imperial College London: Astrophysics, Theoretical Physics
• Kings College London: Theoretical Particle Physics and Cosmology
• Lancaster: Observational Astrophysics, Theoretical Particle Cosmology
• Manchester: Astrophysics, Theoretical Physics
• Newcastle: Astrophysics & Observational Cosmology, Cosmology & Quantum Gravity
• Nottingham: Astronomy, Particle Cosmology
• Oxford: Astrophysics, Particle Theory
• Portsmouth: Institute of Cosmology and Gravitation
• Queen Mary, University of London: Astronomy, Numerical Relativity (Maths)
• Sheffield: Gravitation and Cosmology (Maths)
• Sussex: Astronomy, Theoretical Particle Physics
• Swansea: Particle Physics and Cosmology Theory
• University College London: Astrophysics, Space and Climate Physics (MSSL)