National Grid supplies the energy for the UK, and also manages the high voltage power transmission system. Each year, they prepare a Future Energy Scenarios report looking at energy needs across the UK and the different alternatives for how those needs can be met. The most recent FES was published in July 2018, and is the source for the figures and quotes below.
Widespread adoption of electric vehicles will increase energy consumption by 30%
The FES includes two possible future scenarios with heavy EV adoption -- "Community Renewables" (envisioning widespread energy decentralization) and "Two Degrees" (focused on a centralized model for limiting global warming to 2C). In these two scenarios, the UK meets the goal of ending sales of gas and diesel powered vehicles by 2040.
This table shows 2017 demand (for all sectors) and expected growth in the transport sector by scenario:
An interesting aspect of the model is that early, aggressive adoption of EVs reduces the total peak demand, because of smart charging and vehicle-to-grid (V2G) technology:
In all our scenarios, peak demand from EVs is managed through smart charging. This behaviour is more evident in our two 2050 compliant scenarios, reducing peak demand by 8 GW in 2030. By 2040 this saving would stabilise at 32 GW.
The increase in electricity demand from EVs will be met mostly with wind power
This figure shows how the generation mix is expected to change in the "Community Renewables" scenario:
You can see that the greatest growth comes in the form of wind (on- and off-shore) and solar capacity, with coal generation eliminated by 2025, and natural gas diminishing to a fraction of its current capacity by 2035. The description in the text reads (emphasis added):
Figure 5.2 shows the annual electricity output of different generation technologies and their carbon intensity in the Community Renewables scenario. Here, the electrification of transport and heat increases demand, leading to higher generation output being produced to meet demand.
By 2030, renewable generation, particularly wind and to a lesser extent solar, makes up more than 75 per cent of generation output. By 2030, the carbon intensity of electricity has fallen to 75 grams of CO2/kWh, and then continues to fall to reach 32 grams of CO2/kWh by 2050.
In the "Two Degrees" scenario, off-shore wind and nuclear make up a larger share, with on-shore wind supplying less, and solar about the same.