Starmer isn't hiding behind that, at all.
He had repeatedly said that he backs the current provisions of the Equality Act that permit for single sex spaces (where reasonably required). He has repeatedly said "single sex" and was has been clear on multiple occasions, including the most recent debate, that people with Gender Recognition Certificates can be excluded, and that he supports that.
This is how the law currently operates and is why transwomen, with GRCs, can be excluded from women's prisons.
If the Supreme Court does determine that sex in the Equality Act means legal and not biological sex, only then the Act would require amendment. Given that Starmer has repeatedly said he supports maintaining existing protections for single sex spaces and supports clarifying legal guidance around their implementation, I don't see any reason to think he would not follow through on that, if the Supreme Court decision requires it.
What you (and Jane) seem to want, though, is for all transwomen to be excluded from all women's spaces. I agree that Starmer won't deliver that (and nor do i expect the Tories would). To repeal the GRA, we'd likely have to leave the ECHR, and I hope that does not happen.