According to
this page the BC27 provides selectable gains of 58 and 40 db. Perhaps that selection is made via a switch that is internal to the unit. I assume that your MC is a low output MC, and you are presently using 58 db of gain.
You would most likely have to use the 40 db setting with a MM or other high output cartridge. My suggestion is that you temporarily change to that setting while your present MC is in place, set the volume control to a physical position that is similar to the positions you presently use (which will of course produce much lower volume than it presently does), and see if you hear the radio station (with no music playing).
I think that should give a reasonably good (although not conclusive) prediction of whether or not going to a MM would resolve the problem.
Good luck! Regards,
-- Al