A lot of heads are very reasonable it and do understand. There is a points system in place which your head will have to complete for each child and if they come in under a certain score, then the hol can be authorised at heads discretion. At heads discretion means just that though, they CAN authorise up to 10 days agreed family holiday per sch year, however a lot of parents fall at this first hurdle when they make the assumption they are entitled to these 10 days agreed hol!!!!
There is nothing more likely to make a head say no, than being told it is your right to the holiday!!!!
However I digress, you could also write to the chair of governors at the school and send a copy to your schools education welfare officer (this is the person that issues the fine if one is to be issued and often getting jn first with them can be a blessing - especially if your head teacher is an arsehole!!!)
One thing to be aware of though, if you do get a fine, don't ignore it. You only have 28 days to pay it or it doubles, and if you continue to ignore it, you WILL be summonses before a magistrate (county court) where you could be fined up to £1000, given an absolute discharge or handed a community sentence or parenting order!
IME if you are making a reasonable request in a reasonable manner, then only an unreasonable person would turn you down flat without considering the situation.
There are various other loop holes too, and I'm happy to share them if need be
some are a bit drastic though!!!! Lol!!!