This extract from a Wikipedia
page explains the background to the origin of a top hat being used as a symbolic reference to a Mad Hatter.
"The Hatter is a fictional character in Lewis Carroll's Alice's Adventures in Wonderland and its sequel Through the Looking-Glass. He is very often referred to as the Mad Hatter, though this term was never used by Carroll.
The phrase "mad as a hatter" pre-dates Carroll's works. The Hatter and the March Hare are referred to as "both mad" by the Cheshire Cat, in Alice's Adventures in Wonderland in the seventh chapter titled 'A Mad Tea-Party'...
...Mercury was used in the manufacturing of felt hats during the 19th century, causing a high rate of mercury poisoning among those working in the hat industry. Mercury poisoning causes neurological damage, including slurred speech, memory loss, and tremors, which led to the phrase "mad as a hatter". In the Victorian age, many workers in the textile industry, including hatters, often suffered from starvation and overwork, and were particularly prone to develop illnesses affecting the nervous system, such as central nervous system (CNS) tuberculosis, which is portrayed in novels like Alton Locke by Charles Kingsley and North and South by Elizabeth Gaskell, which Lewis Carroll had read...
The Hatter introduced in Carroll's Alice's Adventures in Wonderland wears a large top hat with a hatband reading "In this style 10/6". This is the hat's price tag, indicative of The Hatter's trade, and giving the price in pre-decimal British money as ten shillings and six pence (or half a guinea)"
Although in the book the label on the top hat is its price, on the pub sign the label has the number 43, which is simply the pub's number on Iffley Road.
The pub was originally called The Cricketer's Arms because it is near to a local cricket ground. There is a stone relief carving of a batsman in front of his wicket waiting to receive a bowl.
These days the pub is a cocktail bar where cocktails are ordered by telephones on tables, and there are live acts in eccentric speakeasy-style bar.
As well as the pub sign there are a number of murals painted on the outside wall of the pub depicting many signs from the book Alice in Wonderland.