The visitors, architects and environmentalists who were attending a conference, plunged into the fountain in Piazza della Repubblica, which is surrounded by five-star hotels and upmarket restaurants.
Four men reportedly stripped nude while the two women went topless when they took a dip in the fountain in the early hours of Sunday morning.
The spectacle of the drunken British tourists stopped traffic around the busy intersection and passers-by called the police.
The visitors, aged between 25 and 49, were charged with committing obscene acts in public, ordered to put their clothes back on and issued with spot fines of 169 ($301) each.
It was just the latest instance of tourists jumping into the city's marble and stone fountains - behaviour which risks damaging the monuments.
In July, with temperatures hovering around 38C, a group of three American tourists stripped off and waded into the Fountain of the Four Rivers in Piazza Navona, one of the city's most elegant squares. On the same night, a group of young Belgian tourists leapt into another fountain, featuring the figure of Neptune, just a few steps away.
Meanwhile, in Venice on Monday, police arrested two tourists after they allegedly stole a gondola and took it for a joy ride on the Grand Canal.
Asked by officers what they were doing, the German tourist and his Polish friend told them: "We just wanted to go for a spin".
