Talk to the secretay/principal of your childrens school also. They can apply for a book grant on your behalf - not a huge amount of money, but it's not means tested and every bit helps.
Also if they have a request for photocopying/arts materials type money - ask if you might have a waiver for this and if there is a book rental scheme in operation it's worth using.
This year's limit for a one-parent family with 3 children is 395.30, not 375.30 (the site may not have been updated as the scheme doesn't start till next week).
As mentioned earlier, you should make an application at the local health centre. If you are refused, you can make an application for an Exceptional Needs Payment, which will take all of your circumstances into account.