Traveller's response is great.

Also send it to your local member and shadow member (and any other parties) for your state and federal parliament, AND mark it clearly on the letter that you're cc'ing it to them all, so they can see who else might be "listening in" to each others' response (or lack there of).

And if there's a Parent/Teacher Committee or similar, send it there too - just in case the school delegates, and it ends up taking weeks for it to get from one desk to the next, and then longer to wait for the next meeting, etc, and then getting lost in politics ... much simpler to send it directly, so noone has any excuses for not replying sooner.

I'd give them 14 days. 7 would be nice, but 14 makes you look perfectly reasonable, as they have time to check it out, have a meeting, determine a course or action, and reply to you.

May also be worth saying something like, "as I have not had any success as an individual parent requesting other individuals to not park illegally, and so I think it is clear that the school or council will need to takea prompt and firm a no-tolerance policy to illegal parking, to ensure all children at [school] are kept safe."

Let us know how you go?