Yes, by law, parents whose children are of compulsory school age (5 to 16) and registered at school are responsible for ensuring that their children attend school regularly. If they fail to do this they may be guilty of an offence and can be given a penalty notice or prosecuted under section 444 of the Education Act 1996.
An Act to consolidate the Education Act 1944. Chapter 56 contains certain other enactments relating to education, with amendments to give effect to recommendations of the Law Commission.
Further information on GOV.UK regarding parents responsibilities and their childs attendance at school.