Yes. The other issue in terms of housing stock is that a lot of the more recent housing stock has nowhere to put a cylinder for hot water, which means it's not practical to use HPs for hot water for showers etc. This either means replacing showers with instantaneous resistive heating-based "power" showers or keeping two systems even if you can retrofit with an air to air HP for space heating - adding cost and reducing savings available.

But the biggest barrier is the relative cost of gas vs electricity in the UK. Gas is about 4x cheaper than electricity per kWh so even with a COP of 4 the efficiency savings will take a long time to pay back capital cost.