Detailed navigator for UK Computer Science Master's?
So, is there a specialised computer science master's course ranking
  website with a column for “philosophical direction” or some kind of
  “business vs academic career” weighting?


No. While it would be nice if there was a system that you could enter your definition of "best" and it would spit out the school for you, it just doesn't exist. While it probably is not a fair system, if you want the "best" according to your grandmother's definition, you probably want to limit yourself to the Russell group. You could also look at the 2008 RAE for what HEFCE thinks is the "best". You can also use league tables. The best approach would be to actually define what you mean by "best". Factors you may want to include are location, course size, research component, course work, faculty, and reputation.