We're also apparently in the process of nuclear decomissioning, and I'm not sure where that lost power will come from.
At the moment, we just ramp up gas-fired power stations to meet demand, so yes, we can just burn more gas to generate more power. In this scenario, transmission/distribution and charger losses wipe out a lot of the CO2 gains.
We also haven't even touched on the idea of commercial EVs - I'm not sure of the figures, but I suspect that the energy requirements for making all vans, trucks, and lorries electrically powered will outstrip EV domestic usage (and, for that matter, should be more important from a CO2 reduction point of view).
[1]https://en.wikipedia.org/wiki/List_of_power_stations_in_Engl...