Pimlico, a few years after the end of the Second World War. London is suffering the torment of rationing and a record-breaking heatwave. Meanwhile, the local people are informed that an unexploded bomb, buried in a local derelict site, is to be detonated.

Local shopkeeper Mr Pemberton tries to attract interest in a scheme to redevelop the site as a children's swimming pool and playground. But as the local council is rejecting his plans in favour of a money-making sale, children playing on the site accidentally cause the bomb to explode. When the local people gather round the crater, Pemberton steps too close to the edge and falls in. Later, he tells his wife and daughter that he imagined he saw treasure in the hole.

Pemberton and daughter Shirley return to the hole, to find a horde of old coins and artefacts, including a portrait and documents, which they later discover relate to the lost Duke of Burgundy, thought killed in battle in the 15th Century.

At the inquest to determine what happens to the treasure, a historian, Professor Hatton-Jones, is summoned to give specialist testimony. The Professor tells the court that the papers reveal that not only was the Duke of Burgundy not killed in battle as had been supposed, but was rewarded by King Edward IV with the gift of a portion of what is now Pimlico. The King's seal was never rescinded, making the residents of the area still, in law, citizens of Burgundy, not Britain, and the treasure the property of Burgundy, not the Crown.

When local bank manager Mr Wix is told off by his supervisor for speaking to the press, and threatened with a transfer, he informs his boss that as the branch is legally in Burgundy, head office no longer has jurisdiction. The implications of this spread along the street, as residents realise they can abandon their ration books and pub licensing laws.

News of the Burgundian secession causes headaches in Whitehall, as civil servants realise that government has no authority on foreign soil. Meanwhile the street is overrun by hawkers and black marketeers taking advantage of the police's refusal to enter the area.

At the advice of the Home Office, the Burgundians form a council led by Mr Pemberton, but are told the body can't be recognised unless its appointment accords with the laws of ancient Burgundy. The cause seems lost until the arrival of Sebastiane de Chavalier, a Frenchman from Dijon, who claims to be the heir to the ancient Duchy of Burgundy. His claim is verified by Professor Hatton-Jones. Meanwhile, HM Customs sets up a border control around the new state. But the Burgundians' delight at this apparent solution is short-lived, when they realise that neither they nor their customers will be able to come and go between London and Burgundy at will.

When the Burgundians board an underground train travelling through their territory and insist that its passengers meet Burgundian customs regulations, the Government closes the border, leaving Burgundy without power or running water.

Sending their children off for the duration of the siege, the Burgundians settle in, organising themselves and sharing resources among the citizenry. In the heatwave, water soon becomes a problem, and the council organises a midnight sortie into England to siphon water from a nearby hydrant into the new swimming pool. The mission is a success, but a tap left on in the pub - acting as the central food store - causes a flood, ruining almost the entire supply.

Defeated, the Burgundians surrender. As they prepare to leave their borders however, the children return, carrying food, which they throw over the barricades. Soon more and more Londoners come to throw food packages from trains and buses. Buoyed by this support, the Burgundians hold out. Negotiations with the crown continue to stall on the issue of the treasure, until Mr Wix, now Burgundy's Chancellor, suggests loaning the treasure to Britain, with the interest going to Burgundy.

A celebration is organised marking Burgundy's return to British sovereignty and the opening of the new Burgundy Lido. Just as Burgundy officially rejoins Britain, the heatwave comes to a sudden end, the heavens open and the temperature plummets.