According to the following quote it was at this meeting, beginning on Tuesday Sept. 10, 1861, held in the Bristol Atheneaum that the Chess Association finally decided to prepend the qualifier British to its name:
After meetings in Liverpool in 1854 and Leamington in 1855 the N&MCCA (Northern and Midland Counties Chess Association) met in 1857 back in Manchester. Here the decision was made to make the organisation into a national one under the somewhat bald title of the CHESS ASSOCIATION. At first this national body held meetings roughly annually: 1858 in Birmingham, 1860 in Cambridge and 1861 in Bristol. In common parlance the word ‘British’ came to be added at the start of the CA’s name, so the 1861 meeting decided formally to adopt the commonly used title of British Chess Association.
— Northern Counties Chess Union (link)
I will be back to revise and update the background and description for this tournament. But, having just completed the tournament using 365chess’ version of the games (<CG> is missing the decisive R1 Kolisch–Paulsen game), plus two stub forfeits by Boden in the final round (held at the Divan in London btw) – here are two versions of the 8-player, 3 round, R1+2/single + R3/triple decision xtab:
First, Chessbase’s version:
(Click on either image to enlarge)