Yes it is true, some people can get a s-ex change on NHS.
It isn't easy, they have to go through many years of counseling, hormone treatment and many other things before NHS will say yes. NHS have to be 100% sure that the person really wants/needs it.
It is also covered here in the US under Medicaid. Some States allow it.
I am not going to get the info for you, google it

I think it is called s-ex reassignment surgery over here. NY State allows it, or did.
Some info about changes in NY State:
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