Hello luckygirl have you put 'writing a petition ' in Google ? I've just tried and there are quite a few links there. Certainly worth a try.
I'd be doing some fact-finding and canvassing opinion now, to gauge the strength of feeling on the necessity of traffic calming measures there . Have you spoken to the police about their call-out rate over the past, say,6-12 months? You say there's a school nearby, will you get support from parents? Etc.
So, I'd say, get all the info you can and then go to meet your local councillor (don't pick the one whose politics echo yours, rather the one with a proven track record for getting things done) and sell the petition idea to them. And then let them do it

Just my first ideas while I'm drinking my first cuppa. 2nd cuppa might bring some more, but honestly I'd say sell the idea to your local mp/councillor and let them run with it.
Good luck!