The National Grid assumption is that engaged customers will use their car batteries to provide a distributed virtual power plant to "plug the gap" at peak times. This process is generally referred to as Vehicle-to-grid (V2G).
The National Grid figures currently assume that only 2% of vehicle owners engage in V2G through to 2030, but that the proportion increases after that, with up to 45% adoption by 2050.
Working on a typical figure of 90kWh for the battery of an electric car, and a typical rate of 6kW at which V2G systems currently operate, each car could provide power for 15 hours. So, if 20% of car owners provide power to the grid using V2G - that's about 6 million cars - a total of 36GW could be supplied for 15 hours. (This assumes that each of those car batteries is fully charged at the start and fully discharged at the end and achieves maximum efficiency when supplying the grid, which is impractical in reality, so a realistic figure would be somewhat less than this.)
If enough electric car owners agree to V2G, and are in a position to provide electricity to the grid at times of need - clearly this means that the car owners won't need the electricity themselves at that time - then V2G could provide at least part of the deficit caused by the use of the main intermittent sources for a period of time.
However, as with all storage options, it would be for a limited time, and in no way could it accommodate long periods (many days or weeks) of very low wind, for example.
Bridging the Gap to Net Zero
The National Grid's Bridging the Gap to Net Zero programme explains in more detail how excess energy produced during periods of oversupply by renewable sources can be used to charge vehicle batteries. Energy stored in the batteries can subsequently be used during periods when renewable sources are not able to maintain supply.
In this programme it is proposed that by 2050 over 75% of GB's 35 million vehicles could be using smart charging, creating the potential for roughly one fifth of GB's solar generation to be stored for when it is needed.