As the installed capacity of residential rooftop PV systems increases in the UK, the likelihood that LV networks will experience periods of unacceptably high voltage or line utilization increases also. Whilst the use of battery energy storage systems (BESSs) for violation management has been explored in previous work, the robustness and cost effectiveness of utilizing existing customer owned BESSs for such purposes has not been extensively examined on UK LV networks. In this paper, we use mixed-integer quadratically constrained programming (MIQCP) formulations to determine optimal BESS takeover for violation control at various PV and ASHP ownership fractions, whilst implementing Monte-Carlo methods to explore the multiple possible technology ownership patterns that may occur at each penetration level. We compare the cost of feasible BESS takeover solutions to the cost of the reconductoring works that would be required to mitigate the same violations, where novel mixed integer linear programming (MILP) formulations are used to determine the optimum reconductoring strategies. We perform the analysis on two models of real urban feeders located in the north west of England, and find that whilst BESS control may sometimes compete economically with reconductoring, BESS takeover control cannot consistently and adequately mitigate violations at the majority of PV and ASHP ownership fractions when BESSs are available at fewer than 100% of PV array owners residences.