I would research childcare options in your local area as you will be in a difficult position if your employer refuses your request. You may need to look a little out of your area but there are many good childminders and nurseries around.
I submitted a flexible working request on the 7the June, I just started chasing it up as I hadn't heard anything. My current hours are full time, I've requested part time, morning shift as I can get free child care mornings, but not afternoons.
Having chased it up they are now asking me to submit a letter with 3 choices and my reasons, I've already submitted a letter with my request. I can't give 3 choices as I can't get child are afternoons so my only option is mornings.