If I purchase two separate tickets for travel on the same day what will happen if one flight arrives late causing me to miss the other flight?

Perhaps to be more clear:
I want to puchase an e-ticket from BMI to fly BRU-LHR and then fly AC from LHR-YYZ-LAX. If my BMI flight is delayed and I miss my AC flight what will AC do? Is this very risky?

Thanks for your help