the birth certificate and passport are not the important factors here - rather it is the matter of parental responsibility that you need to consider. If you were / are married to the mother then your child was born you will have automatic parental responsibility, this would mean that in theory you would need to agree to allow your child out of the country. If however you were unmarried then parental responsibility varies depending on the circumstances e.g. The law regarding whether you have automatic parental responsibility when unmarried changed in 2003,
http://www.fnf.org.uk/pro.htm
the site above gives a good general introduction.