Free healthcare in UK?

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The linked article in your post while not technically inaccurate is rather deceptive. It's essentially an opinion piece although it does quote from a more accurate article. Seven year-old children referred to the clinic are provided with counseling not medical intervention. There is a huge difference.
From the article:

 

Yes, wherein ‘counseling’ breathes life into social conditioning. Or you don’t actually think they’d discourage transitioning in this climate, do you ?

Add: this climate … J.K. Rowling Erased From Museum’s Hall of Fame Over Views on Gender – The Daily Sceptic