We can get a fair idea from Theresa May's pronouncements and from the Scottish consultation documents what the proposed new GRA might look like.
The proposals are to remove all the requirements for evidence. Applicants will no longer have to show they have a diagnosis of gender dysphoria or that they have 'lived in' the new gender for 2 years (in practice a few official docs in the new name - passport, drivers licence, DWP, HMRC letters, payslips, household bills etc.)
The proposals don't just change an administrative procedure for those who would have applied for a GRC anyway, they expand eligibility to anyone with £140 and a biro (fee waiver for anyone on a low income). It's true you'll also have to pay a solicitor's fee to notarise the stat dec. A quick google shows the going rate for this service is £5.
Aside from prisons, the GRA makes little practical difference these days and the EA exceptions can be used to keep spaces and services female only even where a tw has a GRC. What the self-ID proposals do - have already done before any legal changes, is change the culture around what and who women are expected to put up with in our spaces (in the widest sense).
Shelters and rape crisis centres are perfectly entitled to use the single sex exceptions in the EA and exclude tw, both with and without a GRC, in order to keep them female only. They're just increasingly less likely to use them because of the cultural change outlined above, and because of pressure from transactivist shits. This is bad for women and girls.
Campaign for your own spaces. If you hurry up you might be in time to get support from women before we've all completely run out of good will.
The other thing to consider is how the GRA interacts with other legislation. It may seem like it makes no difference to allow people to self-ID to get an obsolete document, but if another law is then amended to allow further rights to people with a GRC we could be in deep shit. For example the trans equality report also recommends changing the equality act so that sex based exceptions would not apply where someone has a GRC. The current government have said they won't change the EA but governments only last a handful of years, after that all bets are off.
the rates of criminal behaviour among self-identified trans people is much much lower than the societal average
Citation please. This is a ludicrous assertion because 'self-identified trans people' is literally anyone who says the magic words.
and there is ZERO respectable evidence that self identified transgender females represent any threat to non-transgender females of any age.
Well, I saw first hand a woman get punched repeatedly in the head by a self-ID'd tw so ...