I recently finished my 21 day pack of my contraceptive pill, during this gap, before I was due to begin my period, I had sex with my boyfriend and the condom split. So just to be safe I went to get the morning after pill. The pharmacist sad that I was unlikely that I would be pregnant but that I should just take the morning after pill in case.

However, that was the day I was due to begin my period( and well within the 72 hours of sex) which was Saturday, it's now Monday evening and I still haven't begun my period. I;m due to start taking my pill again tomorrow but am unsure whether too as I haven't had a period. Or should I wait until after I begin my period to start taking my pill?

Go see your GYN. Your system sounds out of whack completely. Have the GYN run some tests so you know what is going on.
Hopefully it will be nothing.