A CFI in the UK context is the Chief Flying Instructor. Basically the person who should set and control the standards of a school/club.
In theory any FI could be the CFI since there is no minimum requirement and no real definition of the role. There is an accepted level of experience however.
An encyclopedic knowledge of LASOR's and an ability to drink vast quantities of Tea/Coffee are pretty much the most important qualities. A good line in "war" stories helps as well!