Distribution networks have been traditionally designed with limited monitoring and controllability. Therefore, most Conservation Voltage Reduction (CVR) schemes have been implemented in MV networks. However, the deployment of on-load tap changers (OLTCs) and monitoring in LV networks creates the opportunity to actively manage voltages closer to end customers, unlocking further benefits. This work proposes an active CVR control scheme that, using limited monitoring, manages voltages in OLTC-enabled LV networks. A stochastic quantification process that caters for load uncertainties is used to assess the active control's annual benefits for different control cycles, considering realistic time-varying household profiles and models per day type and season (l-min resolution). Results on a real UK residential LV network model demonstrate the inadequacy of the well-known CVR factor to assess advanced control schemes. More importantly, the proposed approach significantly increases annual energy savings compared to fixed or active primary substation voltage reductions, regardless the control cycle.