Excellent and important article, James. I got into something of an argument a year or so ago with a social worker who insisted to me that LGBTQ people can always adopt if they want to. I tried to explain to her why that's often not the case, but I didn't do as good a job as you just did here.
On another note, I don't know about the UK, but here in conservative parts of the US, LGBTQ people already have a certain stigma to overcome with social workers and state agencies, who may not overtly discriminate, but who are often not disposed to favor same-sex couples in general for adoption.
Throw in two or three of the complicating factors you mention, and it's often game over.