I still don't understand why a conservative government would be interested in getting this legislation through? Why now, what triggered it and what's in it for them? Is it 'the government' as a whole or some individuals driving it?
This is a brilliant question. I can't answer it fully (I don't think anyone can TBH), but I'll have a go at some of it
After the Coalition government legislated to allow same sex marriage (something championed by the then Conservative PM, David Cameron, and Maria Miller MP) a number of LGB lobbying organisations found that they had almost worked themselves out of existence: the big thing that they were working for (and fund raising for) had been achieved. Then more and more often, LGB organisations became LGBT (and LGB officers became LGBT officers etc etc), and suddenly there is purpose again to the likes of Stonewall.
Hopefully one day we will be able to look back and see why TRAs have been so successful so quickly, as it is somewhat of a mystery. On the face of it, it's because they have been very successful at infiltrating government (so schools are directed towards dangerous organisations like Mermaids and GIRES for training, for example) and they are good at social media. The money trail would be very interesting to follow
What do the government get out of it? Well, the narrative about "being on the wrong side of history" for saying things like "children should be allowed to be children" and "women don't have dicks" is very pervasive, and politicians generally care very much indeed about legacy. TBH I can't work out why Maria Miller is so supportive or TRA demands, given that she is a lesbian, but it's worth remembering that the Committee that she chaired and which recommended self-ID only took oral evidence from TRA groups and individuals - no womens' groups or GC transpeople were invited to speak to the Committee.
I think it's individuals within the Government who are driving this, but until recently many MPs had simply not engaged with the issue, seeing it as something of a minority interest, side issue that had nothing much to do with them Thankfully, over the past few weeks that is starting to change, and people are waking up to the far-reaching implications of self-ID (and some of the wilder TRA claims and demands)