Your Medical Sex But Societal Gender

When the NHS announced that they will be working towards same sex hospital wards, the inevitable question was always going to be what about the transgender patients and they shot back with the perfect answer, they will base it on their biological sex.
There does seem to be much confusion around a persons sex and their gender which are two very different things, your sex is determined by what set of Chromosomes nature gave you but your gender can be whatever you decide you want it to be and no medical procedure can change your chromosomes so when i was growing up what we called a 'sex change' was actually a gender change, you can chop things off or have things added but your sex is going to be the same because you have an X or a Y.
It was explained to me a long time ago that Medical science has a pretty clear definition because as well as the most common pairings, you also get XXY, XXX, X and XYY but simply if there is no Y Chromosome present, its female, if there is one then it's male so you could have as many X's as you liked, XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXY if it was possible but that one Y would mean male and because the female is XX and 50% of the chromosomes comes from the mother, one of them has to be X which is why it is impossible for humans to get a Y or a YY.
Gender on the other hand means you may look, sound, act or even have the genitals of the opposite sex, the World Health Organisation defines your gender as 'the socially constructed characteristics of men, women, boys, and girls that relate to biological sex' which is a bit woolly but kinda means your gender is whatever you decide your gender is and not what society says it should be based on socially agreed-upon characteristics and that is when we get into the whole thorny world of public bathrooms and pronouns.
I am therefore fine with medical bodies basing a persons 'sex' on their biological make-up, i could turn into a man tomorrow and start wearing mans clothes and even have genital surgery but i would still have the internal workings of a woman which could need to be dealt with medically and i wouldn't be getting a prostate anytime soon.    
The bottom line is that the boundary between a persons sex and their gender gets confused and you may get someone on a hospital wards who considers themselves a woman but is biologically 'male' and would prefer to be on a female only ward but that is a question for society to answer around same gender wards because it is rightly up to each individual to determine their gender and their choice should be respected but when it comes to the NHS and medical issues, your sex is decided in the womb and medically you would treated as male or female depending on the internal workings of your body.