Apologies there are some changes on their website when I checked today..
If the application is made within one year of birth of child as per above-mentioned process and subject to fulfilment of the eligibility criteria as per Ministry of Home Affairs guidelines, the High Commission shall register the birth of the child as an Indian citizen and issue the Birth Registration Certificate. In cases, where applications are made after one year of birth of child, the process is same. However, applications will be forwarded to Ministry of Home Affairs for their approval. Thereafter, on receipt of approval of Ministry of Home Affairs, the High Commission will register the birth of the child and issue the Birth Registration Certificate.
Check this link for more information:
https://www.hcilondon.in/birth_registration.html