What do families do when young children say they have been born into the wrong body and want to change sex?

Camille is six. Today she is wearing a dress patterned with strawberries and a pink zip-up sweatshirt with Dance printed across the front in sparkly sequins. Her fingernails are painted alternately pink and blue. She likes playing with Barbies. Her favourite Disney heroines are Elsa from Frozen and Ariel from The Little Mermaid.

Camille was born a boy. For the first few years of her life, she was known by her parents as Sebastian. When you ask Camille if she can remember being physically male, she nods her head. “Everyone was calling me Sebastian, but I was a girl,” she says, placing all the emphasis on the word. “I used to have girl pyjamas with Minnie Mouse on them and I used to sleep in them.”

Camille is one of a growing number of children who experience gender dysphoria – the belief that there is a mismatch between their biological sex and their gender identity. It is estimated that between 2% and 5% of the population experience some form of this, although statistical analysis is patchy.

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In Britain no major government or administrative surveys have included a question where transgender people can choose to identify themselves, but it is thought that there are between 300,000 and 500,000 trans people in the UK.

Camille lives in Napa, California, with her parents Eduardo and Casey Leon, and her story features in Transgender Kids, a BBC2 documentary presented by Louis Theroux, which airs on Sunday night. In the US the treatment of transgender children is arguably more accepted and advanced than it is in the UK. While the NHS does treat transgender children as young as 12 with drug therapies, most GPs will not prescribe hormone blockers to delay the onset of puberty until a patient is 16.

Camille, by contrast, has spent the last two years being assessed by psychologists at the child and adolescent gender centre at the University of California in San Francisco, where a group of pioneering medical professionals are helping children to begin changing at ever younger ages. Treatment includes psychological counselling, hormone blockers and, eventually, the possibility of sex reassignment surgery.

Critics have queried whether these children are too young to make up their own minds and whether, in adulthood, they might wish to reverse the process – by which stage it could be too late. But for Casey, 33, that concern is misplaced.

“You spend a day with my child, and tell me I don’t have a little girl,” she says. “She was never Sebastian, she was always Camille ... We kind of knew at 18 months. She really loved wearing my shoes, she was into more feminine things. We would put a truck in front of her and she would just not care about that very much.”

As a boy, Camille was visibly unhappy. She would have tantrums. Getting her dressed in boy’s clothes in the mornings would be almost impossible. At the age of four, Casey recalls, her child started asking “to become a girl”. Her parents took the decision to allow her to wear female clothes. Then they asked their child’s elementary school to start referring to her as Camille. At home they started using female instead of male pronouns. Almost immediately, the tantrums stopped.

“We now have a happy kid who is a good student and amazingly creative,” says Casey.

Although Camille is too young to be considering drugs or surgery, the Leons are in no doubt about the journey that lies ahead. “For me, I just see it [surgery] coming,” says Eduardo, 32. “Because the way she acts whenever she gets undressed and gets into the shower, it’s like she hates it [her penis]. She hides it. She doesn’t want us to see it. She’s embarrassed of it.”

Do they miss the idea of their son? “I don’t think so,” says Eduardo. “I love my kid, no matter what. The only thing that kind of makes me sad is that she didn’t play soccer.”

And what about Camille? Does she think she will ever change her mind about being a girl and want to go back to being a boy? Camille shakes her head and removes a dangling necklace from her mother’s neck. She slips it over her head and starts playing with the silver charm. “No,” she replies firmly.

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For Nikki and her family (who do not wish to give their surnames), the feelings were equally strong. Nikki, who was born male, recalls wanting to dress in female clothes by the age of three. At 11, she was praying that she would wake up being a girl “and that no one would remember me as a boy. I actually did that a lot. I used to talk to myself quite a lot about wanting to be a girl and my mum would hear me.”

When she was 12, she watched a documentary on transgender children and had an epiphany: “I didn’t know much about what this thing transgender was. I just got really kind of excited that there was actually something that could change me. I guess, after that, I kind of told everyone about it.”

Now, Nikki is 14 – a gangly, awkward, beautiful teenager – and has been on hormone blockers since 2013. Initially the drugs led to mood swings. She felt increasingly emotional and some friends fell by the wayside. At school in north California, she was teased and called names.

Her younger sister, Danielle, found it difficult to come to terms with her older brother changing gender. In the documentary, Danielle explains: “I was the only girl in the family. I wanted to be the first to wear makeup … I didn’t want anything to change.”

And yet, despite the trauma she faced, not once did Nikki question her decision. She was “excited” about starting her transition, she says, rather than scared.

These days she has a “natural” relationship with her younger sister and 10-year-old brother, Matteo: “It’s not a big deal for us.” She even lets Danielle borrow her hair straighteners.

Does Nikki want surgery in the future? “Yeah, I really do. I’m not in a huge rush for the sex reassignment surgery, but I know I want to do it, maybe some time in college or after that … I won’t be able to have biological children, but I want to be married, I want to have kids.”

Nikki’s parents, Isabel, 47, and Jerry, 45, are supportive of their daughter’s journey. At first, Jerry concedes: “I did not have an idea of what to do. It was: how do we navigate here? There was an option that we should proceed with caution and not let this happen, but …it becomes evident it’s not a very good direction to take. It leads to all the wrong things, all the things you don’t want your child to go through – lack of self-esteem, not being their natural self.”

Indeed, last year a UK survey of more than 2,000 people conducted by Pace, a mental health charity, found that 48% of transgender people under 26 said they had attempted suicide. Confronted with such grim statistics, Jerry started to see Nikki’s transition as a “no-brainer”.

“I see it as protecting the life of my child,” he says. “And that’s how I justify what I’ve done as a father.”

Several hundred people undergo sex reassignment surgery a year in Britain, but there is a long waiting list for NHS treatment and the number of referrals is substantially higher. Research from the US and the Netherlands suggests that up to a fifth of patients regret the change, but such statistics are hard to quantify or monitor.

Isabel admits there are still moments of sadness. One of the most emotional moments came when Nikki’s sex was altered on her birth certificate. “I have a lot of memories of her as my baby boy,” says Isabel. “It was a grieving process for me. I was sad.” She wells up. “And sometimes I’m still sad.”

Nikki, however, is completely sure of what she is doing. What would she reply to someone who asked how she could accurately know her own mind at 14?

She squints, giving a shy half-smile. “How would I not know my own mind?” she says. “I’ve been like this for a couple of years and I love it. I would never change back. If I had stayed as a boy, I honestly wouldn’t even know what I would do. I wouldn’t even go out. I don’t think I would make it.”

Back in Napa, Camille is tiring of the tedious business of being asked questions about something that seems self-evident to her.

When she imagines being older, she says she automatically envisions herself being a girl and then a woman. So, what does she want to be when she grows up? “A mermaid,” she squeals excitedly. It seems as good an answer as any.

Transgender Kids will be broadcast on Sunday night on BBC 2 at 9pm