This study quantifies the increase in the peak power demand, net of non-dispatchable generation, that may be required by widespread adoption of heat pumps. Electrification of heating could reduce emissions but also cause a challenging increase in peak power demand. This study expands on previous studies by quantifying the increase in greater detail; considering a wider range of scenarios, the characteristics of heat pumps and the interaction between wind generation and demand side management (DSM). A model was developed with dynamic simulations of individual heat pumps and dwellings. The increase in peak net-demand is highly sensitive to assumptions regarding the heat pumps, their installation, building fabric and the characteristics of the grid. If 80% of dwellings in the UK use heat pumps, peak net-demand could increase by around 100% (54 GW) but this increase could be mitigated to 30% (16 GW) by favourable conditions. DSM could reduce this increase to 20%, or 15% if used with extensive thermal storage. If 60% of dwellings use heat pumps, the increase in peak net-demand could be as low as 5.5 GW. High-performance heat pumps, appropriate installation and better insulated dwellings could make the increase in peak net-demand due to the electrification of heating more manageable.