I don't know but I don't think so. It is the Supreme Court (not the EHRC) that authoritatively determines the law.
So, once the Supreme Court rules on something then that is the law.
The EHRC’s role is to provide guidance to assist people to understand and comply with their rights and obligations under the Equality Act 2010; its role is not to determine the law or to interpret the Equality Act.
This is laid out in the Equality Act 2006.
It was also referenced in a 2018 case, City of York Council v Grosset [2018] EWCA Civ 1105 at [42] and [68], .