The best are the Royal College of Art and Central St. Martins in London.
In Scotland the Glasgow School of Art has a great reputation as a leading institution in art teaching.
I would personally recommend the NUA, Norwich University of the Arts, to study Graphic Design, Bristol University for Animation and Falmouth University for Illustration.

According to the Complete University Guide (CUG), the top 3 Uk universities for art and design are Edinburgh, University College London (UCL) and Oxford. Out of all 75 universities in the guide, the lowest ranked is Bradford.

The CUG bases its rankings on a great many factors including grades, student satisfaction and graduate employability. It's considered reliable by many students, but it shouldn't be taken as the last word, as you need to consider other things too.

Firstly, are you thinking of studying a particular art specialism? If so, it's a good idea to type the name (eg 'fine art' into a search engine with the word 'university' and see what comes up. You could also talk to a careers officer at a local school or college.

Also, what other things are important for you, for example, location, cost of living in an area? If you narrow down your options as much as you can, this will make it much easier to choose the right place for you. Good luck.