This is c and p'd from the first UK lawyers site that came up on google:
"Because of increasing instances of child abduction in custody cases and a growing number of children who are victims of trafficking and pornography, an immigration officer, airline or travel company may ask you to provide a Travel Consent Form if your child is traveling internationally with only one parent or with another adult, such as a grandparent, uncle or aunt.
In an effort to prevent international child abduction , many governments have initiated special procedures for minors at entry and exit points to their countries. These often include requiring documentary evidence of relationship and permission for the child's travel from the parent(s) or legal guardian (s), not present. Having such documentation on hand may facilitate entry or departure. To be of full effect, this document should be sworn and signed before a Notary Public Lawyer.
"Sole Custody" means that only one parent or guardian has the right to make decisions affecting the child. "Joint Custody" means that both parents have the right to participate in making these kinds of decisions. Parents may have Joint Custody even if the child resides with only one parent.
If you are a single parent (by divorce), in addition to the travel Consent Form which must be signed by the Notary Public Lawyer, you will require the long version of the Birth Certificate and a copy of your Custody Order, Judgment or equivalent.
If you are one parent traveling alone with your child, you need the Travel Consent Form to be signed by the absent parent. The Travel Consent Form must include the absent parent's address, telephone number, authorisation to travel, the destination and length of stay.
Travel Consent Forms which are sworn and signed before a Notary Public are required for single parents (by divorce)and minor children to travel to France, Spain, Germany, Australia, China, The Dominican Republic, Japan, Canada, Chile, Dubai, India, Sri Lanka, Taiwan, Mexico, United States of America and Vietnam to name a few. "