If I have it right the first digit in the FE should be a 6, 7 or 8 (1956, 1957 or 1958) and they changed to FC with the new model.
Most 1958 built FCs also have an "8" prefix on their chassis number. This was changed in about December 1958, because it was recognised that the numbers were overlapping with 48 series cars, and a decadal system was clearly insufficient. Kind of a Y2K style problem in miniature.
Because only a small number of cars were manufactured between 19 November 1948 and 31 December, there were not a lot of FC models with chassis numbers that duplicated those of 48-215 cars from a decade earlier, but from 1949 onwards, the situation was clearly going to get messy, hence the move to model code and sequence and factory code.