I don't think you can search for birth entries online if they are were less than 100 years ago.

Marriages 75 years
Deaths 50 years

https://geni.nidirect.gov.uk

"For data protection reasons, if you are using the internet to search the register, some of the records will not be available to view. You will be able to access the following records:

• birth records over 100 years old • marriage records over 75 years old • death records (including World War II death records) over 50 years old

You cannot access civil partnership and adoption records online. If you want to view these records, or view recent records, you must book an appointment at the public search room or, if you know the details, you can apply online for certificates."