You do not usually need permission to teach your child at home. However, if your child is already at school, you should first tell the school in writing that they won't be going to school. The only time you need permission to take your child off the school register is if they go to a special school.
You don't need special qualifications to teach your child at home, and you don't have to follow the national curriculum. However, you must make sure that your child is educated suitably for their age and ability and for any special educational needs they may have. If the local education authority does not think you are doing this, they may send you a school attendance order (see 'When must my child go to school?')