Birth certificates for England and Wales, until 1969 did not have a space to enter a surname for the child. This example from 1913 for Northern Ireland shows a similar format:
http://www.claires-rosleaancestry.co.uk/dads%20birth%20certificate%20full.jpgAs you can see, only the child's forename/s go in the place marked 'Name, if any'.
The registration appears on the birth index under the parent's surname, or the mother's if there is no father recorded.
This means that for a birth registration of an illegitimate child to appear in the index under the father's surname, either the mother has to present herself falsely as if married - giving her name as eg Mary 'Father's surname' formerly 'Mother's surname' - or the father has to be present at the registration and agree to have his name recorded.
In the second case, the child's name appears in the index twice, once with each parent's surname.