The Supreme Court is not a consulting body. It exists to interpret the law as laid down by Parliament.
It hears legal argument from those bringing the appeal and the respondents.
Sometimes interveners will apply to be heard on pertinent points also. Whether or not their application is accepted is also based on established law.
EHRC and Sex Matters have oral evidence; Amnesty and a combination of lesbian groups gave written submissions.
No trans groups applied to be heard.
You might ask yourself why on earth not. Where were Stonewall, for example? It's really no good crying foul about not being included after choosing not to put yourself forward.