The building served as Venice's embassy to Rome between the 16th and 18th centuries.
Campaigners issued their demand to the Italian Foreign Ministry last week in a letter from the movement's "plenipotentiary minister of foreign affairs".
It said the handing over of one of Rome's grandest palazzos would mark "the beginning of a good relationship between our states, as there was in past centuries".
Curious as to why a copy of the letter had also been sent to the letters pages of the Sunday Telegraph, the newspaper contacted the plenipotentiary minister, Giovanni Dalla Valle, to find out more. He turned out to be a consultant psychiatrist living in Tonbridge, Kent, who was born in Italy but has lived in Britain for 22 years. "Please call me a spokesperson, those titles are just symbolic," said Dalla Valle, 50, seeking to play down images of medieval diplomats wielding quills.
The campaigners want independence not only for the lagoon city of Venice but also its hinterland of Veneto, where wealthy manufacturers have long been receptive to calls for independence. They are angry that 2.1 billion ($3.4 billion) of the region's taxes are spent elsewhere by Rome. Gianluca Busato, who organised the referendum, is urging local businesses to stop paying taxes to Rome and the group have set up a 10-member council.
While they are not trying to hold meetings at the Doge's palace in Venice yet, Mr Busato has his eyes on an impressive castle known as Castel Brando, perched on a rock in the Dolomite mountains. Many observers in Rome are laughing. "Of course it's ridiculous," said Sergio Rizzo, a columnist for the newspaper Corriere della Sera. "Anyway, as the European Union pulls together, how can countries start losing bits and pieces?"
But the council's historian, Paolo Luca Bernardini, 51, argues that the existence of the EU is precisely why new mini-states could survive and said: "With free circulation of goods and people inside the EU, why do we need a central state that drains funds from us?"
The movement has not been without its hiccups. On April 2, police arrested 24 campaigners - none of whom were on the council - accusing them of trying to turn a tractor into a tank, with a cannon. Investigators said the aim was to drive the tank into St Mark's Square in Venice.
The arrests were a handy excuse to stop a protest rally by the Northern League, the once powerful separatist party humbled by scandals, which is looking for a comeback ahead of the European elections.
Bernardini, a university professor, denies living in a fantasy world, citing independence movements in Scotland and Catalonia as evidence that the time is right for Venice.