Up until next week I work for a company that supplies software to wholesale energy generators, consumers and brokers, so all this sits a little in my bailiwick. Prepare yourselves.....
TL;DR;
It's complicated.
The long version - settle yourselves down.
Despite the hype about battery technology, power (electricity) can't yet be stored in quantities that make a large difference to the grid, so has to be generated as required. Pumped hydro facilities like Dinorwig Power Station in Wales do store power, but these are usually used to meet peak exceptional demands and have a high associated market price.
This means that power has to be generated as required and there needs to be sufficient capacity in the system to meet demand. The UK power system (the grid) operates as a market where Generators (people with the power stations, turbines etc) agree to supply Suppliers (wholesale energy providers like the 'big six') with a certain amount of power at a certain time, based on forecasts of requirement. This can happen literally years in advance, but continues to be refined with better forecasts as a particular point of delivery approaches. The price for these longer term contracts is agreed between the generator and supplier based on a private contract.
There are also open markets and auctions to buy and sell future power generation capacity. The prices on these markets are driven by the usual supply and demand 'rules'.
The important thing about this mechanism is that, although the generator and supplier have a bilateral arrangement, the actual power generated at the required time is not delivered to the supplier. Instead it's put on the grid and taken off by whoever needs it.
The problem with this is that, if any of the suppliers hasn't forecast their requirements correctly (and they won't!) or the generator can't produce the power then there may be a glut or shortage of power on the grid. This leads to an unstable supply, brown outs, power cuts, riots and zombies.
All hail the 'System Operator' aka National Grid. It's the system operator's job to balance the supply and demand at short notice across the grid. To manage this, generators are required to report their final expected power generator an hour before the time of delivery. Some generators can also offer to generate more (or less) at short notice at a price to tweak the power on the grid and balance the system. This is known as the Balancing Mechanism. When delivery time comes, the System Operator will ask selected generators to modify their output to match supply and demand based on price, but also generator characteristics (how quickly can they fire up) and sometimes location.
The point of all this waffle is that what makes a good source of power isn't just the amount of power that can be generated. This market mechanism was implemented around 2000, when renewables were an insignificant part of the energy mix. Although there have been revisions to the various pricing and engagement mechanism, the market is still biased (IMO) towards traditional energy generation sources that can provide predictable output at any given time. For example, the economics of nuclear power look very shaky in terms of price per unit, but the market 'likes' a source that chugs away at 800MW day and night as it provides a baseload that can be bought and sold years in advance. Wind and solar are both capable of generating power at lower cost and fewer subsidies, but the market as it's currently constructed probably hasn't worked out how to fully handle the unpredictability (or cost-in environment impact in any real sense, but that's another debate).
Ignoring environmental concerns, the gold standard is still gas, as it can generate large amounts of power predictably AND ramp up and down generation at short notice, something nuclear can't do and you can only do with coal with difficulty (I think Drax has a mechanism, but that's second hand 'knowledge').
So, when it comes to where your electricity is coming from, there's a crude hierarchy of engagement as demand ramps up...
Nuclear and coal (always-on, fixed generation 'baseload', price is hedged long-term)
Renewables (difficult to predict availability, complex pricing but potentially low)
Gas (available, predictable and responsive, more volatile market pricing)
Interconnectors (buying excess power from our European chums)
Short Term Stores (can only deal with demand peaks, usually expensive)
As of Q1 2018, Gas was the UK's largest source of energy (36TWh), followed by renewables (19TWh) and Nuclear (15TWh).
Electricity comes at a cost. If it comes from fossil fuels, that is what an electric car is using. The fossil fuel generating station might not be on your doorstep, but it's on somebody else's. Efficient small petrol/diesel engines use less fossil fuel than "eco" electric ones. Sometimes the electricity might come from wind, hydro, or nuclear, but it's probably from oil or gas.
I'd maybe agree with the first two sentences but the last bit is contentious at best. Taking all my waffle above, electric cars ARE a store of power and so can take advantage of periods of low demand to harvest excess renewable generation if it's available. I believe Norway has a scheme that allows electric car owners to sell their car change back into the grid at peak periods if they don't need to use the vehicle.