TFA's claim is offshore wind prices are 40% cheaper than gas.

The parent comment stated "actual cost has to price in the impact of using it". Most people would agree on this. However, for both claims to be true, the collected tax revenue must be spent offsetting the impact of that gas usage - not simply reducing gas usage (ie. that consumed gas isn't being compensated for).

If the UK government is spending that tax revenue on anything it wants, then it's not the actual cost, is it?

Sorry I don’t follow. Why would the taxes need to be spent offsetting anything? The carbon reduction already happened, because the taxes made this auction choose lower emission alternatives.

If you then also spend the taxes on some form of offsets (if we pretend for the sake of argument that those work) you would have reduced emissions twice. One time seems plenty to say they are doing their job.