If the parents of a child are not married, the mother does not need consent from the father to travel abroad. It doesn't matter if his name is on the birth cert.
Permission from the father is only required only if the father is a legal guardian.
If he is legal guradian, then his permission also has to be sought to obtain a passport for the said child and also has to be signed by both solicitors.
If hes not legal guardian, then mum can do go where ever she wants with her child and not have to seek 'permission' from the father.
All children under the age of 16 now require their own passport - they cannot be put on a parents one any more. It's a bit daft really as my 3 year old boy definitly does not look like his passport photo taken when he was 6 months old!