If the house is in one person’s name, and they separate, does that mean that the person that has the house in their name can ask the other to leave the property immediately?
The answer is “No”. Prior to a marriage breakdown (which includes the death of one spouse, separation with no reasonable prospect of reconciliation, and divorce), property is governed by the normal rules i.e. by title where it is determinable or other proof of ownership of a particular asset. When a marriage breakdown occurs, the question of equalize of property comes into play.
Even if a house is not jointly owned by the parties in a marriage, if they have lived there on the date of separation, it becomes a matrimonial home. A matrimonial home cannot be sold or encumbered without the written consent of the other spouse, regardless of how title may be held. Without written consent, the sale or mortgaging may be set aside by a Court. The Court has power to award exclusive possession of a matrimonial home to either spouse, including a non-owning spouse. Even if one spouse moves out, until an order for exclusive possession is granted, the spouse remaining in the matrimonial home cannot exercise the rights of exclusive possession, such as changing the locks.