In a medium saucepan, combine the heavy cream, milk, and sugar. Heat the mixture over medium heat, stirring occasionally, until the sugar has dissolved.
Remove the pan from the heat and stir in the toffee pieces. Allow the mixture to cool to room temperature.
Once the mixture has cooled, pour it into an ice cream maker and churn according to the manufacturer's instructions.
Once the ice cream is finished churning, transfer it to a freezer-safe container and freeze for at least 2 hours before serving.