Damn - The proposed change in the law (which no-one has seen because it hasn't been drafted yet) won't make any difference at all to anyone's access to public toilets or changing rooms.
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 as' 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.
Strictly speaking, a GRC is neither here nor there for trans people legally, aside from a couple of very specific situations. It's almost obsolete. 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).
The other thing to consider is that 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.
I'm sure I've had this exact exchange with you very recently, possibly on this thread 
By the way, did you know that some christians consider 'damn' to be a really bad swear? I've met christians who consider it far worse than words like piss, shit, fuck, cunt, prick, tits or arse.