I found this definition of a Davenport in the Urban Dictionary:

"The word used, in particular by grandmas and those from the south, to call a large sofa, typically brown and furry. The sofas are "L" shaped and decorated with doilies and cheeto dust. Itchy blankets don the arm rest and occasionally orniry cats emerge from in between the cusions. When used in this sense, it is commonly pronounced "Damport"
2) A town in Iowa
3) More simply put, a couch "

However, in England a Davenport is more likely to be a kind of writing desk.

I have now been wondering about the people who were neither posh nor trying to be posh (referring to people maybe forty or fifty years ago). What would they have sat on? Would it be a divan? And rather than pudding would they have had a "sweet", or maybe just "afters"?