Thomcat -
My dd (9months) just received a pack after a check up with the Health visitor which contained two reading books in a smart calico book bag with information on how to join the library in her own right - as others have said - no overdue fees for her and no problem if she decides to chew the book - just return it and there will be no problem. There was also a laminated placemat with rhymes on it. ( sounds similar to what meanmum has said but I am in essex so I figure it must be where you are too)
Looking at the bag it is done by 'Bookstart' and there is a website to go with it - perhaps you can find out if it is in your area..
www.booktrust.org.uk
Hope that helps Thomcat