At home I use 15,000kWh of oil for heating each year (about 10kWh per litre, 1500 litres), and 8,000kWh of electricity (we use a lot more than the average household). For driving that's another 5000kWh a year if at 4 miles per kWh.
So even in a residential context, electricity is only about 1/4 of the demand. Across the whole country it's less than 300TWh out of 1500TWh, under 20%.
That excludes "imported energy" though, as in goods which used energy to make but were then imported.
The heating and driving could theoretically be electrified, though it might or might not make economic sense.
Which will increase demand
Driving can push up the low points (charge cars overnight), but heating would put a lot of demand in winter months, meaning a day time cold day in January with no wind will require a lot of dispatchable electricity, at night time in September with a gale blowing wind will be providing almost all the demand.
Nuclear doesn't really help as it's more expensive than the wind when it's windy and demand is low, and its impossible to build enough to cover the peak January demand unless you spread the fixed cost over the entire year, which means getting rid of every other form of electric production, and you'd still end up paying more per kWh than you would with other forms of storage.
Nuclear can't survive in a free market. It can't scale up to provide for areas of high demand, low supply, and it can't scale down to be affordable when there's high supply and low demand.