Sure - EV owners charging over night will increase demand a lot, but National Grid would rather that was during the night, than add it onto day use.
Charging overnight means it's not being used/ added onto the current day demand.
e..g
- Current peak day demand is about 25GW
- If you have majority of EV's charging in day (say 20GW) then peak day demand increases to 45GW, which means commissioning new power stations to meet the increase in day demand. This costs a lot of money.
- Set an overnight low tariff price and people with EV's will charge during the night. That 20GW of charging has no additional impact on the Grid capacity, because it's not higher than the demand in the day. (The number of power stations required for day and night use is the same).