I definitely agree that if it's thrown back to the government, it will be harder for them to stick nothing to see here.
The Telegraph/IPSOS ruling that makes in sport can be referred to as males is helpful. Other newspapers will either go to IPSOS with their own submissions or publish anyway and wait to be damned. There is nothing so successful at getting the media on side as telling them no.
The SP case has also had wider recognition and not only is there more to come, but there is a queue of other cases to raise awareness further. Less captured reporting, will again be helpful.
If the Supreme Court concludes anything other than a woman in law is the biological variety, the press will be all over it and it will be a massive talking point everywhere. The LP can't hold the traditional red/blue wall if they deny biology. Outside metropolitan bubbles, people simply don't buy it.
And much as I hate to say it, the Trump factor comes into play too. Starmer won't want Trump/Musk/Vance to be able to say that they don't know what a woman is in the UK.