If they feel they don’t want the child to be government property then that’s their right as parents.
Legally they don't have a right to not register their child.
And registering a child doesn't make them "government property".
Best case scenario, this will be problematic for the child when seeking official services in life such as healthcare, benefits, passport, employment, education. The child may also be receiving an inadequate education as nobody is checking, and presumably hasn't received preventative healthcare such as screening and vaccinations. At some point the child will need some kind of official input, eg seeing a doctor, and the longer this is left the harder it will be to resolve and the more the child will have missed out on.
Worst case scenario, the parents are neglecting/ abusing the child, and nobody will find out. You can't tell this from the outside as a family friend.
Of course if the child pitches up to A&E unwell they will be treated, but everyone is identified via NHS number or other details, if the child doesn't exist officially this will be identified. Perhaps the parents will delay seeking medical care if they know this.
If the parents don't want to live in a country where registering your child is legally required, they are welcome to move overseas to a country with limited state oversight of it's citizens - but I think they would find living in Somalia or similar unpleasant and perhaps realise that the state has benefit in the UK.