can you not unscrew the actual fan from the plate, turn it around, then screw back onto the plate? that is generally the option for reversing 240v fans.
where does the "single core" terminate? in the ceiling rose or the wall lights?
the reason why i am asking is because we are getting confused with your terminology, 3 core/single core etc. are we talking twin and earth for the 3 core and twin and earth for the single core but with one wire cut...