Incidentally you can no longer put children on parents' passports. They have to have their own passports.
To apply for a child's passport you need to send (originals, not copies):
• 2 new <a class="break-all" href="https://www.gov.uk/photos-for-passports" rel="nofollow" target="_blank">photos of your child</a>d_
• the child’s full birth or adoption certificate (the one with parent’s details on it)
• proof that your child has British nationality (for example a British registration certificate, parent’s passport details or parent’s birth certificates)
• any valid passports from a different country belonging to the child
• any court orders (for example, that describe parental responsibility or residency arrangements)
In the GoFundMe set up by Freddie's mother, it says: "Due to outdated English laws, SJ (now almost four) still does not have a birth certificate."