According to the UCAT website, the following UK universities use the UCAT in their admissions process:

University of Aberdeen, Anglia Ruskin University, Aston University, University of Birmingham, University of Bristol, Cardiff University, University of Dundee, University of East Anglia, Edge Hill University, University of Edinburgh, University of Exeter, University of Glasgow, Hull York Medical School, Keele University, Kent and Medway Medical School, King’s College London, University of Leicester, University of Liverpool, University of Manchester, University of Newcastle, University of Nottingham, Plymouth University, Queen Mary University of London, Queen’s University Belfast, University of Sheffield, University of Southampton, University of St Andrews, St George’s University of London, University of Sunderland and University of Warwick.

The following non-UK universities also use the UCAT in their admissions process:

American University of the Carribean, Poznan University of Medical Sciences, UniCamillus  - Saint Camillus International University of Health and Medical Sciences, St George’s University (Grenada).

This list was taken from the UCAT’s official website. It can be found by clicking on this link.