I just had to look up that claim, and it seems that Turing admitted a homosexual relationship during a police investigation about his house being burgled, seeing as that relationship was with the accused burglar. That's slightly different to the implication that he walked into a police station of his own free will and promptly signed his own castration order.
My description of his conviction was incomplete. I wasn’t trying to give a comprehensive account. I was simply trying to explain the level of protection his privilege afforded him.
He was comfortable reporting one of his lovers to the police because he was used to people looking the other way.
Obviously, one of the many downsides to criminalizing harmless behavior is that it places people outside the protection of the law.
https://en.m.wikipedia.org/wiki/Alan_Turing#Conviction_for_i...
(I'm aware of wikipedia fallibility but I'm on mobile and will generally trust in the citations for this particular individual)