Are you talking about copyright on the book or on the movie?
"Chitty Chitty Bang Bang", by Ian Fleming, was first published in 1964 by Jonathan Cape in the UK. As I understand it, that publisher is now part of the Random House group.
There
is a copyright on the book. (If you look at the book at Amazon or Amazon UK, you will see this.) and I am pretty sure it would cover John Burningham's illustrations of the Ian Fleming novel.
If you have any doubts about using illustrations from this book, I would suggest you contact the publisher and ask permission.
The difficulty I had here, was finding out who owns the copyright in the UK. There are several different editions of the book, all with different publishers.
Often, an author or illustrator will initially own the copyright, but sign it over to the publisher. Random House in the US is probably your best first contact here. They list the book as one published by them.
Here is their permissions page:
Permission for using material owned by Random HouseAs a follow up idea, try contacting the publishers listed at
Amazon UK for UK permissions.
Hope this is of some help.