One day, Mr. Veneering decides that he is going to run for a spot in the British parliament. So he runs around asking all of his high-class friends if he can count on them for support. They all agree and then run off to tell their own friends.
One endorsement Veneering really wants is from Lord Snigsworth, a rich and powerful relative of Mr. Twemlow. But Mr. Twemlow is way too intimidated by this man to ask for such a favor, so Veneering backs off.
As always, Dickens uses his time with the Veneerings to make fun of how superficial and delusional the people of high English society are.
In the end, the campaign is a success and Mr. Veneering gets himself a spot in parliament.