That is a very common and overly simplistic view of the UK's energy market. What you have described is essentially the UK's day-ahead and spot energy markets. The whole point of those markets is to ensure demand is met with near 100% certainty. Setting the price to the last bidder is not unique to the UK for energy pricing, if it were not present then everyone would be speculating what the threshold would be and giving high bids and it would make the market unstable. There are other markets in the UK that behave very differently (such as the ones that green energy companies use to buy 100% renewable energy 6 months ahead of time).
In practice UK electricity prices _are_ much cheaper from wind and solar energy, most of the time, because virtually all of that capacity in the UK was built under what is known as a CFD (contracts for difference) basis. The exact mechanism is a bit subtle [1], but in essence renewables built that way have a fixed price per unit of energy (usually for 20 years after construction). This price is less than what the gas energy producers typically bid in the UK.
The reasons why electricity prices are still on average very high in the UK is because the rest of the energy market is _so_ exposed to gas prices and renewables can't produce electricity a lot of the time (because it's not always windy, and it's not always light outside). Renewable production is highly correlated with itself and not necessarily aligned with demand.
The UK also has other structural problems in the electricity system that have arisen from its exposure to renewables that come with associated costs. For example wind turbines in Scotland often get paid to _turn off_ because their power can't be transmitted to the south of England where it can be used - there are similar constraints with North sea production. Wind turbines and solar panels replacing traditional coal power stations means that the electricity grid has lost a lot of its traditional load balancing and stability mechanisms (conventional power plants provide a lot of stability because large rotational mass synchronised to the grid frequency provides inertia in the entire grid - wind turbine rotation is independent of the grid frequency). ESO now has to have more drastic and expensive mechanisms like demand reduction and rapid response hot reserves in-place. A lot of these issues are transient and will get cheaper over time, but they've become acute in the short-term with the UK's rapid grid decarbonisation.
[1] they get paid directly from the day-ahead, spot, and other markets at the last bidder price. But they either have to refund any amount over their fixed price, or they receive a top-up from the energy companies so that they effectively got the fixed price.