Taking your child out of the country for a holiday or otherwise depends on a few factors including whether or not there is a court order in place.
Under the Child Abduction Act 1984, it is a criminal offence for a parent to take a child under the age of 16 out of the UK without the appropriate consent. Fail to get permission and you could be jailed for child abduction.
If you do not have a court order in place then you need the permission of everyone who has parental responsibility.
If you have a child arrangements order which states that the child should live with you, then you can take them abroad for a maximum of 28 days without needing to gain permission from the other parties with Parental Responsibility, unless the court order says that you can't or places a restriction on taking the child or children out of the country/jurisdiction.
You can take a child abroad on holiday if there is a Specific Issue court order in place allowing you to do so. In order to obtain one, you will need to prove to the court that the trip is in the best interest of the child. Go to court prepared with your date of departure, date of return, means of travel and other pertinent details, including background information on your separation.