For anyone not familiar with the project aims it's worth reading the earlier threads that Stumbledin linked to.
The following summary I've linked below is by the KCL law department to lay out the justification for the project. I've pulled out some key points.
It reveals that you've guessed it- a) Stonewall were on the advisory group and b) a "draft reform bill to focus further policy and wider public discussion on the legal regulation and recognition of gender identity in England and Wales" is supposed to be produced.
As a major piece of law reform research, this project is intended to significantly contribute to debates about gender identity reform. While current agendas focus on the experiences of people whose birth gender does not "fit", this research addresses more broadly the implications of reforming a binary legal structure currently anchored in gender designation at birth.
Also:
Many representatives from stakeholder groups have already agreed to participate (see Pathways to Impact).
Where do these representatives come from I wonder and what are these "stakeholder groups"?
A) Advisory Group (AG): Including representatives from the EHRC, Stonewall and EDF. It will meet at key stages to advise on research design, dissemination, and assessment of research methodology. Members will also assist in reaching research participants.
This gives an idea of what they are intending to facilitate and why Stonewall is on the AG for this academic legal research exercise.
3. GOVERNMENT, PARLIAMENT AND LEGAL PROFESSION. The Women and Equalities Select Committee report on Transgender Equality (2016) recommended comprehensive action including addressing needs of people who identify as non-binary. Given the timing of this project, its research findings are ideally placed to influence future legal and policy debate. The research team will work with specialist lawyers, and policy-makers (including on the AG) drawing on research findings to respond to proposed law reforms and, where necessary, outline alternatives for government departments and shadow ministers.
https://gtr.ukri.org/projects?ref=ES%2FP008968%2F1