Do you have 'parental responsibility'?
If you married to your ex-wife at the time that your child was born, you will have parental responsibility. You will also have parental responsibility if your child was born on or after 01/12/03 and your name appears on the birth certificate. (That date applies to England. It's different elsewhere in the UK). You might also have been granted parental responsibility by a court (or acquired it by other legal means).
If you have parental responsibility, your permission is required to change your child's name by deed poll, until he/she becomes 18 (not 16):
http://www.clsdirect.org.uk/en/legalhelp/leafl et31_6.jsp
Chris