All my initial answers would be literature and story telling based - though geography (location of biggest cities and counties) too.
Far more important in reality is practical knowledge - in very general terms how does the tax system work, how to access the education system and how it's structured, British CV writing expectations, how public transport works, how to call for the emergency services, how to access health care.
On the literature and story telling:
Fairy tales (most "British" fairy tales are broadly European but the Anglophile versions, late obviously exported to other English speaking countries, can be quite markedly different (look at the German version of Cinderella and the central role of her dutiful tending of her mother's grave and the tree).
So fairy tales, nursery rhymes, modern classic children's books like Julia Donaldson, the most famous Roald Dahl, also secular versions of key Bible stories like the Nativity and Noah's ark, the prodigal son, Lazarus, sermon on the mount - not for religious or moral reasons at all but because like fairy stories, nursery rhymes and the most well known children's books they form a backdrop to how many people think and are referenced endlessly in both high and popular culture.
Then a very basic idea about the works of Chaucer, Shakespeare, Austin, Dickens...