Four days in September
The fire broke out in the night of September 2, 1666, at a baker's in Pudding Lane, and was not out until the 5th or 6th, depending on the account. Crowded timber houses with overhanging upper floors carried it from street to street; St Paul's Cathedral caught fire on the evening of the 4th. The toll fits in three numbers: 13,000 to 13,200 houses, 87 parish churches, and some 80,000 people left homeless, against a surprisingly small number of recorded deaths, about sixteen (Britannica, History.com, Insurance Museum).
No house was insured against fire. The contract did not yet exist in any form a homeowner could buy.
The physician who sold rebuilding
Nicholas Barbon, son of a Puritan preacher and trained in medicine, made his fortune rebuilding London. According to the Insurance Museum, he opened an "Insurance Office for Houses" behind the Royal Exchange as early as 1667 and ran it until 1680, when he recast it with new partners and 40,000 pounds of capital as the Fire Office (Insurance Museum, Insurance Hall of Fame). The London Museum holds policy no. 1403, dated August 7, 1682 and signed in his hand, one of the very few that survive (London Museum).
The Fire Office did more than pay. It kept a company of men to put out fires at insured houses, and nailed a metal plate, the fire mark, to their fronts so its brigade would know which houses to defend (Museum of London, Wikipedia). The insurer understood from day one that preventing a loss costs less than paying for it.
What the fire taught the trade
The lesson of 1666 is not that a house can burn: everyone knew that. It is that a single event can burn every house at once. An insurer that had covered each house in the City would have received, in four days, every claim it could ever have. This is the accumulation problem, which still sets how much a portfolio can carry: you can only pool risks that do not burn together.
Cyber ran into the same problem three and a half centuries later. A software supplier shared by a thousand companies plays the part of the timber lanes of Pudding Lane: one failure, and a thousand policies are triggered together. Cyber catastrophe models look for what the streets of 1666 showed to the naked eye: the path by which fire passes from one house to the next.
This page tells a story; it says nothing about what anyone should insure today.