It's a good question. To be honest, I'm still trying to get my head around how the UK electricity market works. Its complexity is definitely a big part of why so many reasonable people can end up disagreeing so vehemently... vanishingly few people understand how the whole thing works (and pretty much none of those who do are listened to by the politicians...)

Your question is good for another reason: you say "price" without qualifying whether you mean wholesale or retail (and, if retail, what individual households pay or what is experienced by industry). A lot of commentators and politicians routinely conflate the concepts to serve their own agendas in order to confuse non-experts.

If one looks first at the wholesale price, you're right that - in general - one would expect it to 'spike' when the gas prices shoot up. But on days when wind is dominant this has a minimal effect on retail prices, because the extra money paid to the wind farms (everybody gets the clearing price) is exactly offset by a reduction in the CfD payment. To repeat: consumers pay the same (high) price for most wind-generated electricity irrespective of the gas price.

So the interesting question, I think, is: what happens on days when the wind isn't blowing and gas generation is dominant? And here's the thing: if the price for gas-generated electricity (with carbon tax to account for the climate externality) is below the CfD strike prices, we're still ahead, even if it has spiked above its average. And because the CfD strike prices are so eye-wateringly high, this happens far more often than not.

Indeed, it was only for part of 2022 that the wholesale price was above the CfD prices and so the wind farms were paying money in to the system rather than taking out.

This chart from David Turver (who I learned a lot of this stuff from) is eye-opening in that regard: https://x.com/7Kiwi/status/2031657347433603581 (edited to provide clearer chart)

If the renewables fleet is supposed to be protecting us from gas price strikes, we're paying a VERY expensive premium for that insurance.