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I wouldn't email, less likely to get into dialogue of why you can't have days off. I would just send note or email week prior politely stating your child will not attend xxx dates. No need for huge explanations. Good luck
If you've got a really good reason why you need to take them out early, rather than cost/convenience, then I think it's worth an email to the Head.
We did this a few years go when DH was working on a project with a go live date at the end of Aug, and there was no way he could take leave in the 6 weeks leading up to it as he was one of the senior managers. We emailed and were given permission to take DC out for a week at the start of July, after the end of year exams.
Similar situation here as in need to be around from 22/8 onwards for GCSE results/aftermath, and also have a mid-Aug committment.
I have spoken to DD2's school and they have led me to believe that taking her out for the last 2 days is likely to be OK - provided her attendance at time of application is at least 95%. She is yr5 though, so maybe primary different?