I am sure this has already been said, but being cynical it could be that the trans debate is nothing but a smokescreen in order to deliberately make it more difficult to collect these statistics and thus perhaps obstruct issues like moving toward equal pay law etc.
It is so obviously necesary to collect these statistics, and the downsides of not colecting so obvious and so significant, that perhaps there is another reason this is even being contemplated, because I don't beleive this is just about transpeople.
I mean, the govt give no such consideration to any other marginalised groups - just look at the way they treat the sick and disabled. So why do they care so much about about trans people? It is would be very out of character for them to care so much to do this for one group.
I don't believe they care about anything other than an economy that keeps themselves and their mates in the money - certainly, I don't believe the majority of the government give two shits about midwives etc or making life fairer for the average and/or poor person.
I personally wouldn't put it past many in the governemnt to be perfectly happy to sacrifice what is obviously very necessary data, in order not to burden big business with having to finally address issues such as equal pay and to benefit from being let of the hook in the future by having inaccurate or unavailable figures.
There is also still a huge section of men (and in the ingrained misogyny in some women) who don't want to relinquish any more of their advantages to women. Combine this desire to see the preservation of their power, the preservation of the their money and preservation of the staus quo, and I wouldn't be at all surprised if some saw this as an opportunity to pursue their own agenda by piggybacking it onto (and exploiting) a 'trendy' cause.
If Brexit goes ahead there will be no redress to the European courts for issues of fairness and discrimination and the govt of the day can do what they like.
You only have to look to America to see that such regression is entirely possible and perhaps much wished for in secret by some/ many/ enough.
Whether you agree with my thoughts or not, there are only 3300 or so signatures so far - we need to do more to get the number up.