This project won't do anything (as you likely already know). The reason electricity is so expensive is because it's tied to gas prices, which is an entirely political decision.
Even if they're typically the same, because CCGT is the best for on-demand generation, flattening the demand curve ought to slightly reduce that marginal cost.
I've seen the UK generation market attacked quite a lot lately, but to me it makes sense to price everything at the marginal cost, and doing so also helps encourage capital investment in generation that can have lower generation costs themselves, because the marginal cost is only slowly impacted rather than a boom and bust model.
Fixed costs and capital costs end up being shouldered by the consumer which ironically ends up pushing overall costs up.
They'll also likely reduce the balancing costs by relieving congestion.
Probably too small to notice among all the other costs and changes, like deploying more renewables and starting to pay in advance for new nuclear.
In the UK I believe it is policy for electricity prices to be high in general for thse reasons and to encourage lower usage.
The issue in the UK is that we moved to renewables that can't produce energy at the margin, marginal prices are still driven by gas, and we simultaneously decided to shut down large amounts of non-renewable sources of energy to satisfy the ambitions of politicians.
Result? Highest energy prices in the world, most energy-intensive industry shutting down, and massive reliance on political direction/regulators by industry (the original comment is not right, since the mid-2010s energy companies have been directed day-to-day by the state, invest in this project, don't do this anymore, etc. Our policy is made by people who wish the world was a certain way, reality doesn't matter to them).
It's the same as they are doing on immigration: They say they want to lower it but the actual policy is to keep it high. People have understood that now, which explains in big part the Conservative wipe out. Labour is now on the same path.
Retail electricity is taxed in the UK.