I'm revisiting some of the younger books at the moment with my one year old. The one she currently can't get enough of is Peepo Baby illustrated by Georgie Birkett. This one is a Bookstart book so is probably very well known!
Peekaboo Baby by Mandy Ross and Kate Merritt. It's a game she loves anyway and the fact it's in a book and she can look under the flaps to find the baby is great fun. These flaps are stuck on and not so sturdy but sellotape is wonderful stuff!
Is This My Nose by Georgie Birkett. The lovely combination of the big fold out mirror at the end and the pointing to body parts always makes her giggle!
There are quite a few more books she likes but these are the ones I have really noticed her engaging with and enjoying.