The relevant regulations in England are The Pupil Registration Regulations (England) 2006.
Education (Pupil Registration) Regulation 8, 2006
Under regulation 8(1)(d), a 'school-age' pupil's name is to be deleted from the admissions register if:
He has ceased to attend the school and the proprietor has received written notification from the parent that the pupil is receiving education otherwise than at school.
No Delay in Removing Child's Name from Register:
The 2006 Registration Regulations do not permit a delay in removing the child's name from the school roll. Please read 12 (3) on pages 6-7 of the statutory regulations. In the case of pupils who are being taken out of school for the purpose of being home educated, the "ground for deletion" is met under paragraph 8(1)(d) when " the proprietor has received written notification from the parent that the pupil is receiving education otherwise than at school." It should be noted that the 2006 statutory regulations specify that these are the necessary and sufficient "ground for deletion" under 8(1)(d).
Paragraph 12(3) reads as follows:
(3) As to the contents of the admission register comprising particulars relating to a pupil whose name is to be deleted in accordance with regulation 8(1)(d), (e),(g),(i) or (m), the proprietor shall make a return to the local authority for every such pupil giving the full name of the pupil, the address of any parent with whom the pupil normally resides and the ground upon which their name is to be deleted from the admission register as soon as the ground for deletion is met in relation to that pupil, and in any event no later than deleting the pupil’s name from the register.
Government Guidance says No Requirement to Obtain Agreement from School or Local Authority
163. School and local authorities should not seek to prevent parents from educating their children outside the school system. There is no requirement for parents to obtain schools and local authorities agreement to educate their children at home. Further information on local authorities’ role in home education is available on teachernet.