One solution for improving the thermal performance of existing building envelopes is the use of pre-formed internal insulative panels that incorporate impregnated phase change materials (PCM). Such measures have the potential to enhance the energy flexibility of buildings when combined with HVAC control automation and digitalisation techniques, thereby offering the possibility of participation in demand side management measures such as demand response programmes. The current literature on building envelope physics lacks research on the integration of such PCMs in building envelopes and advanced HVAC control automation, especially in the context of research into the energy flexibility and demand response nature under heating and cooling scenarios. The aim of the current study is to evaluate how the addition of PCM impregnated internal wall panels and HVAC thermostat control automation affect both the thermal performance of the building envelope, as well as the wider building energy characteristics, when subject to different demand response events. The reference building is a detached residential house which has a floor area of 160 m2 and a south-easterly facing aspect. This study presents a building energy management methodology to develop new energy flexibility indicators for HVAC thermostat control automation taking into consideration a pre-cooling period prior to the demand response event as well as evaluating the thermal energy storage capacity and peak power curtailment. Four different demand response scenarios are examined. Simulation results show that shorter envelope pre-cooling periods in association with longer demand response periods are preferable for all envelopes to achieve the maximum power curtailment for cooling. Gypsum boards enhanced with PCM were retrofitted as part of lightweight thermal mass and medium weight thermal mass envelopes and are shown to give best cooling demand shifting and performance. It is concluded that for energy flexibility scenarios, the pre-cooling length should be always less than the length of the demand response event to ensure higher cooling efficiencies.