Travelling with children
Just a few points to consider when travelling with children as there are strict laws across the world to try and stop child trafficking and abduction.
The UK Government states that 'You must get the permission of everyone with parental responsibility for a child or from a court before taking the child abroad. ' If you are travelling alone with your child they suggest carrying a letter from anyone else with parental responsbility. For details of what to include in the letter see here.
If you and your children have different surnames you may be stopped and questioned at passport control. It may be sensible to take your child's birth or adoption certificate with you to prove your relationship. This isn't compulsory but might make the process a bit smoother.
If you are taking someone else's child abroad you are advised to carry a letter of consent. Here is a draft letter of consent you can adapt.
Some counties have really strict laws about entering or leaving a country with a minor even if both parents are present. South Africa, Botswana, The United States and Canada are some of that have tight regulations. See the relevant embassy for up to date information. Here is a link to all the Foreign Embassies in the UK.
Here is the UK Government link with all the details you need to know about taking a child abroad - Permission to take a child abroad.
Finally, while all this stuff sounds very formal and a bit scary, thousands of people travel every day with children in the above circumstances and have no problems whatsoever - just be prepared!