It is the LEA who decides if there should be a fine, not the HT. Things were tightened up in 2013
Schools used to have the discretion to allow up to 10 days' term-time holiday each year in 'special circumstances'. The rules were tightened in Sept 2013 though – now head teachers at state schools in England can only give permission for term-time absences in "exceptional circumstances".
These could include visiting seriously ill family, attending a close family member's funeral or if a family member's in the Armed Forces and returning from operations. The Department for Education says you're "unlikely" to get permission simply for a family holiday.
There are also a number of allowances made under the law stating when your child can be absent. These are if they are sick, they are off for a day for a religious observance, they have no fixed address or if the child doesn't live within walking distance of the school (for under-eights this is two miles, for over-eights it's three miles) and the local authority didn't provide transport, boarding accommodation or the option for them to go to a closer school.