(A). A long clay pipe, such as churchwardens used to smoke some half a century ago when they met together in the parish tavern, after they had made up their accounts in the vestry, or been elected to office at the Easter meeting.
“Thirty years have enabled these [briar-root pipes] to destroy short clays, ruin meerschaums, and even do much mischief to the venerable church warden.” —Notes and Queries, April 25th, 1885 p. 323.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Churchwarden from Infoplease: