Little Tiger Press is one of my favourite picture book publishers as they are so approachable (by post) and always reply to submissions. And they have such a lovely website with good advice for authors! They even have free stuff for children, such as pictures to colour and this cute screen saver.
They publish picture books for the 0-7 age range and stories must be no more than 750 words. As with most picture book publishers, an author only has to provide the words and they match them with a suitable illustrator. They also accept submissions from illustrators.