The legal argument the UK Government made is based on a different issue.
When the Equality Act was written, it brought together a number of separate anti-discrimination laws. It was clear from the beginning that such a comprehensive anti-discrimination law protecting all kinds of different groups would have to carefully balance competing rights, because there are many times when two groups can have conflicting interests. (That's why there are over 1000 explanatory notes that belong to the Equality Act showing how the Act works and how competing interests should be navigated.)
One such conflict was recognised to be between those protected under sex and those protected under gender reassignment, and those in the latter group who had legally changed their sex with a GRC.
A lot of this balancing took ground away from women, i.e. those who most heavily depend on being protected on the basis of sex.
This was justified on the basis of the then prevailing understanding of the group protected under gender reassignment as primarily transsexuals and those with gender dysphoria yet to transition. The argument was that this group is so small and their needs so desperate that any compromise will impact few women in reality but bring a much needed benefit to those transsexuals.
The Scottish Government's GRR Bill upsets this carefully calibrated balance. Now neither argument applies - the numbers are now big enough to affect many more women and the needs of this group, who are neither transsexuals nor suffering from gender dysphoria cannot be said to be at all desperate. In fact, no argument can be nor has been made what that need is, given that this law is no longer about those who identify as trans, but everyone. All of us are eligible now. And no reason has been given as to why we all must be allowed to legally change sex if we have no identifiable need to do so.
What was carefully balanced before, and a justified unfairness to women (justified by the lawmakers, unfair in the views of many women), is now going to be completely out of whack. An unjustified unfairness to women for the benefit of any man was never how the Equality Act was supposed to work in practice.
And that's why the UK Government says that the GRR Bill is having a negative effect on how the Equality Act works in practice.
(The Equality Act also improved the situation for women, because for the six years from when the GRA was passed in 2004 to when the Equality Act was passed in 2010, sex-based exceptions did not exist.)