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I’m not sure I’d go as far as saying electricity prices are pegged to gas prices, but yes gas is still the major fuel source used to generate elec in the UK, so an increase in the cost of inputs (gas) will lead to higher prices.
That percentage has been falling for some time though as renewable sources come on stream, but energy is a global market (like oil) and not just UK/EU focussed.
One of the reasons for the big increase in electricity prices is that they are stupidly tied to gas prices. Gas is one of the ways we generate electricity and is v. expensive (well, the price they pay on the European market is expensive, which accounts for around 20% of what we use I think), hence the price hike.
If they didn't peg electricity prices to the price of imported gas, we wouldn't be in this shit. Nuclear (apart from the eye-watering upfront costs) and renewables are still incredibly cheap ways of generating electricity. They could pretty much do this overnight, but it would mean gas-powered generation plants take a pretty big hit. Ofgem is required to ensure the market doesn't fail, which doing this might bring about, so instead we all get hit with massive bills.