Part of the answer lies in the way the wholesale market works. Many (all?) suppliers like to offer their customers the option to purchase energy on a green tariff, and so they need to purchase volume from renewable generators.
Demand for such tariffs is quite buoyant, and since the actual available volume is limited, the market value of green energy is pushed up. This gives investors the motivation to pump money into building more renewable generation - hence the continuing construction of massive off-shore windfarm projects like Dogger. So although the generation cost of wind/solar isn't going up like gas/oil, higher demand is still pushing the price up
For the consumer, it means that if you want renewable energy you either have to be prepared to pay a premium, or be happy with a contract that says something like 'we might have to buy fossil energy if we need to' in the small print.
This can lead to quite a high additional cost. I get my energy from Ecotricity who are absolutely dedicated to only generating or sourcing renewable/low carbon energy and investing all their profits in building more. As a result I am paying £0.40/KWh for my power. If you are on a 'Green' tariff that is charging you much less than that, then it means they are topping up with energy from fossil generators when they need to.
How do suppliers ensure they can provide renewable or low-carbon power? By buying long futures, hedging their supply out absolutely as far as they can, and/or by operating renewable generation resources themselves (vertical integration).
Of course, once the power is in the grid, there's no differentiation between the electrons. All the suppliers are really doing is selling you the services necessary to figure out how much you've used and sending you a bill.
As for carbon capture, there are certainly some small-scale proofs of concept in operation such as the one in Iceland, but it seems pretty clear to me that it's nowhere near cost-efficient enough to enable coal fired power stations to be run cleanly, otherwise there would be people pouring money into developing more of them, especially as the cost of wind and solar is dropping so fast. When it's so cheap to use solar and wind, why bother with the complexity and cost of carbon capture?
https://en.wikipedia.org/wiki/Levelized_cost_of_electricity
