If the father does not have parental responsibility, you don't need his permission to take the child out of the country. (Having his name on the birth certificate will only give the father automatic parental responsibility if the child was born after 01/12/03 in England or Wales, or after 15/04/02 in Northern Ireland, or after 04/05/06 in Scotland. Otherwise he would require a court order to acquire parental responsibility).
If the father has parental responsibility but you have a residence order, you can take the child out of the country for up to 1 month at a time without requiring the father's consent.
If the father has parental responsibility and you don't have a residence order, you can't take the child out of the country without the father's permission.
If you require the father's permission, a simple letter from the father should suffice. e.g.:
"To whom it may concern: I, Fred Bloggs, grant permission for my son, Ronald, to leave the United Kingdom on 26 July 2008 for a period of 42 days, in the care of his mother, Mary Smith. Should any relevant authority require me to confirm this permission, my contact details are as follows: . . "
http://www.ips.gov.uk/passport/apply-child-rul es-parental-responsibility-rules.asp
Chris