Price is set at the margin. Take a look at this graph: https://www.economist.com/img/b/400/507/90/media-assets/imag...

If demand decreases, the supply/demand intersection will switch to the next highest cost producer. Or the same thing could happen if the supply of cheap electricity increases.

Everybody who shops around has a 100% renewables tariff. What that tells you is that most UK consumers don't shop around. This was more remarkable before prices spiked, because previous to that the actual price you paid was usually much lower if you shopped around, and yet they also threw in "100% renewable" because it costs basically nothing. Now the only price it makes sense to pay is the price the government guaranteed, so shopping around is pointless. Which is fair, that was the reality anyway, the companies "selling" electricity exist only on paper, they aren't laying cables, or building power stations [similar companies in the same corporate family might but it's not important here] they just have a spreadsheet basically.

Anyway, the reason it's so cheap to give the few people who care 100% renewable electricity is that the people selling the electricity get effectively paper "It's renewable" tokens which they can sell separately from the electricity, they're called REGOs.

So say I make 10GWh of wind energy today, I get 10GWh of REGOs. I sell my electricity for the same grid market price as the gas electricity or coal power†, or whatever, nobody cares electricity is fungible, and I also sell my REGOs for very little because they're almost worthless, to Very Green Energy Co.

That huge industrial site near you which makes stuff (I know, they do exist in the UK they just don't employ many people any more). They consume 15GWh of electricity, they don't care where it comes from, maybe it's from me, maybe it isn't, electricity is fungible, who cares. They don't care about the REGOs, they just need electricity.

People like you, in your house, consume 5GWh of electricity. Again, electricity is fungible, so who cares where it came from, maybe it's gas, but Very Green Energy Co. have 10GWh of REGOs, so they can assure you that you're all getting renewable energy.

† Actually the Subsidy rules mean I might sort of sell for a different price, but we'll ignore that here, it doesn't clarify this situation at all.

As a consumer you can't in the UK choose to be fully exposed to price fluctuations, which would completely destroy you. You can choose to be partially exposed, it's very expensive right now, but can be cheaper in some periods. It's a risk, take only if you understand it, Octopus Energy are the people to talk to.

Your bills go up because of supplies of all sources of energy not meeting demand as well.