There are two very noon traditional masters degrees issued in the United Kingdom.
Cambridge and Oxford Master of Arts
Both of these universities will upgrade holders of their Bachelor of Arts degree to a Master of Arts award 3-4 years after the person has graduated with their Bachelor of Arts.
Edinburgh University
Where English Universities (Cambridge and Oxford) issue Bachelor degrees at the end of three years of Study. Edinburgh University has a 4 year undergraduate degree which leads to students graduating with a Master of Arts as their first degree.
Over the past decade the Scottish Universities have started to follow the international trend of 3 year (undergraduate degrees), however Edinburgh University still offer a four year MA as a first degree.