To be able to switch courses, you must have done the core modules of the other course, and get a relatively high mark (2:1) standard in these modules.
Since MORSE and Math share most common first year modules, then to switch from:
Math to MORSE - do Probability B, Mathematical Programming 1, Introduction to Quantitative Economics in first year
MORSE to Math - do Introduction to Abstract Algebra, Differential Equations A, Geometry and Motion in first year
This is also probably why the MORSE entry requirement is now shifting to match Math's entry requirement.