There is indeed no requirement to send a child to school. Parents can educate them at home and, if this is done, no checks are made to ensure that minimum standards (or indeed any standards) of education are achieved.
However, if a child is registered to attend a school then Section 444 of the Education Act 1996 makes it an offence to fail to secure the regular attendance at that school.. The Act can be viewed here:
http://www.opsi.gov.uk/acts/acts1996/ukpga_199 60056_en_27#pt6-ch2-pb1-l1g441
If the Local Education Authority (LEA) believes an offence under S444 has been committed they may issue either a fixed penalty notice or a summons to attend court. A fixed penalty notice need not be accepted and instead the parent can ask for a court hearing. The maximum fine if convicted in court is �1,000.
�Leave� of absence may be granted by school heads, though a more robust stance is being taken by some LEAs in response to the large amount of term time being currently lost due to parents taking their children out of school for holidays. They are removing the head�s discretion to grant leave and this seems to be what has happened in your daughter�s case.
My advice (if you want it) is to avoid taking this matter to court. If the LEA has a robust policy on absences for holidays in term time that is their right. The fact that no exams are imminent is not relevant. Children are required to attend for the entire term. Your daughter will almost certainly be convicted of an offence if she does take the child out of school having been warned not to do so and subsequently refuses to accept a fixed penalty. The result will be a criminal conviction and costs of considerably more than �80.