Regardless of whether you are married spouse or a common-law spouse, the end of the relationship is deemed to be a separation. In BC, the date of separation is generally considered to be the date when one spouse coveys to the other spouse, either through words or actions, of their intention to end the relationship permanently.
Two spouses can be separated but still be living in the same home (just as two spouses can be living in separate homes but still be in a relationship together).
If you are married and you have separated from your spouse, you must take the additional step of legally ending your marriage by applying for and obtaining an order for divorce from the Supreme Court of British Columbia. You must have been separated from your spouse for at least one year before a court will grant you a divorce. Also, if you have children, you must prove to the court that you have an arrangement in place with your ex-spouse (either by way of a separation agreement or a court order) for the care and financial support of the children, as the court will not grant the divorce until they are shown a copy of the agreement or order.