Throughout the documentary - which premiered at the trendy New York film festival Tribeca in April - McConnell openly shares personal details including his attempts to get pregnant, giving birth and footage of his child's face.
To promote the short film, which is set to air on the BBC later this year, McConnell shared the trailer in social media posts, where he revealed his child's gender.
In April, two months after the initial court hearing, he gave an interview to The Guardian - where he works as a digital journalist - revealing his own full name, where they live and specific medical details of his transition process.
At a hearing at the beginning of May, the president said it was "striking" that McConnell chose to exclude information of the documentary from the initial court proceedings, telling his barristers: "That is to misunderstand the process entirely."
The president concluded that McConnell had not acted to deliberately mislead the court.
McConnell's dispute against the Government was first reported by The Telegraph in February this year, when his lawyers argued that it was a breach of their transgender client's human rights to force him to be recognised as the child's mother.
The court heard how McConnell completed his gender transition several years ago and was able to access a sperm donor 10 days after legally becoming a man. As a result, he became pregnant and later gave birth to YY.
The evidence prompted Sir Andrew to raise concerns about transgender men's ability to access fertility treatment in the UK, as he called on the government to review the current legislation.
When McConnell went to register the birth, the GRO - which has been responsible for registering births, deaths and marriages since 1836 - rejected his request to be the child's "father" on the grounds that he carried and gave birth to YY.
Lawyers on behalf of the government argued that this is "justified" by the need to have a coherent scheme for the registration of births and the "right of a child to know the identity of the person who carried and gave birth to him or her".
However, as the president was due to hand down his decision on the case, details emerged of the documentary, prompting The Telegraph and several other national newspapers to challenge the Order protecting McConnell's identity. The media groups did not seek to have the anonymity order in respect of the child lifted.
Lawyers argued that McConnell was "trying to have his cake and eat it" by restricting elements of his story, namely the court proceedings, being published in newspapers, whilst openly revealing in detail the story of his journey to becoming a man and the conception and birth of YY.
Gervase de Wilde, representing the media, said the documentary "radically changed" the circumstances of the case and urged the president to lift the anonymity Order to defend the principle of open justice.
"During these proceedings, there was an elephant in the room - the film," de Wilde said. "You do not need legal qualifications or to understand the intricacies of the Human Rights Act to know that it may have some relevance to the court proceedings.
"There should not be any chipping away at the principle of open justice."
