sorry but your employer may find out by a number of reasons
1) NT tax code 2) London gazette or regional newspaper 3) OR writing and asking specific question relevant to income or job description (rare but they can do).
as you may have read you are restricted certain types of employment whilst BR.
If you work for a larger company you may want to speak to your staff association, they may already have someone in the company who is already BR.
it was a hard step for me but i have informed my employer before i was due to go to court, suprisingly they have been supportive