On a cold winters day households are likely to have their electric ASHP heating on throughout the day whereas now approx 20 millions UK of homes are heated with gas. Yes, if you charge your battery off peak and use it during the day you can spread the load but that means the majority of householders have to invest 1000s in batteries. BUT It wouldn't have worked in the past week as there was very little renewable generation to charge the batteries in the first place.
With everyone charging their EVs overnight there may not be an off peak period.
This is probably the golden period where those who can afford perhaps £20K to install solar and batteries (taking advantage of substantial grants) to offset peak usage with their cheap off peak storage. When the grants stop and enough people are doing the same the advantages for saving money may evaporate.