The effectiveness of Conservation Voltage Reduction (CVR) in reducing energy consumption depends on the instantaneous load composition in the network which is affected by the types of customers. This work investigates the benefits from adequately considering residential customer types and their corresponding time-varying models in obtaining realistic CVR estimations. A Monte Carlo-based methodology for CVR assessment considering demand uncertainties is presented and applied to two real UK residential LV networks which have two types of customers: Domestic Unrestricted (no storage heaters) and Economy 7 (with a meter providing fixed hours of supply for storage heaters). The results show that the adequate modelling of Economy 7 customers, i.e., considering the resistive nature and fixed period of operation of the corresponding storage heaters, leads to larger energy reductions. Consequently, considering only Domestic Unrestricted models in LV networks with high proportions of Economy 7 customers can significantly underestimate the potential CVR benefits.