The genesis of the book is well documented. It was a spontaneous act on a summer afternoon; a tale invented to entertain three little girls during a long boat trip. The participants recorded their memory of the occasion - that Carroll made up the story as they rowed along the river. It was not a carefully planned attack on Oxford personalities.
Carroll used real places and events to add to the interest of the story. He also included all members of the boat's crew, slightly disguised, to add to the fun. Dodgson (Carroll) is the Dodo, Robinson is the Duck, Alice is Lacie, Lorina is the Lory and Elsie, and Edith is the Eaglet and Tillie.
Carroll was an observer of human behaviour; the eccentricities of people amused him, such as a man who sold hats by wearing them and a shopkeeper with a bleating voice. But the joke was lost if Alice and her sisters didn't know who he meant. To suggest that the mad tea party was a satire on the Christian Socialists is nonsense.
John Tenniel, Carroll's illustrator, almost certainly contributed allusions to real people; no one doubts his depiction of Gladstone and Disraeli as the Lion and Unicorn in Through the Looking-Glass. But this is a much later personal interpretation, probably condoned but not invented by Carroll.
(Editor of Lewis Carroll's unexpurgated Diaries)