I have a couple ideas. I'll list them below.
The Benandanti:
This is more of a hypothetical idea, since therer isn't really any proof the benandanti came to London. However, with a bit of added details i think this could work well. The benandanti were members of an agrarian visionary tradition in the Friuli district of Northeastern Italy during the 16th and 17th centuries. They claimed they could leave their bodies when they went to sleep, and during this time they could leave their bodies and fight/talk to spirits. During the years 1575 to 1675, many of the benandanti were accused of witch craft (As this was when the witch trials were going on) and put to death by the Roman Inquisition, however it has been noted that this period was rather historically 'boring' as the benandanti weren't killed as much since the Inquisition wasn't as interested in them, however groups were still tried and convicted of witchcraft. An interesting idea could be a group of benandanti escape to England on the run from inquisitors, in the year 1666. Maybe the benandanti come to London in secret (As, historically speaking, there isn't really any proof benandanti came to London). An idea could be the protagonist accidently finds the meeting. As the benandanti were seen as a cult, this could go along well. The protagonist could overhear a conversation of burning the city down, as to free spirits trapped under cursed land, or maybe 'cleaning the land of sin', and so the protagonist tries to warn people but no one listens. Maybe the benandanti hurt/kill people he's close to, to get him to keep quiet, and so the problem becomes personal. Eventually, it can all escalate to the protagonist battling the cult leader as all of London is engulfed in flames. (This idea could easily be replaced with some other extremist group or cult around the 1660s as well, just thought the benandanti would be interesting subjects).
The Second Anglo-Dutch war:
The Second Anglo-Dutch war went on between 1665 to 1667, between the English and Dutch Republic for control of the seas and trade. Since this war is a large conspiracy as for why the fire began, you'll already have a bunch of ideas to mess around with if you wanted to look it up a bit more. Basically, this war was mostly naval. A common theory is that it was started by the dutch. Reports came of people seening men throwing fireballs, or custom grenades, at certain buildings when the fire started. This eventually turned into mob violence, where people would attack any dutch or Frenchmen they saw in London. Maybe your protagonist is actually a bad guy, and he's the one who threw grenades and started the fires. Another idea is maybe the protagonist sees his father or brother getting beat up by a mob, so he goes on a mission to find the real culprits. Maybe these villains actually are Dutch, or maybe it was started by a naval officer who used to have a lot of power in the government, but lost his position and became a ship captain instead. The captain started the fire only to get revenge on the house of his superiors that denoted him, but accidently set everything on fire, or maybe he purposely set all of London on fire instead. The protagonist eventually faces off with the captain/whoever started the fire.
I'm a big history nerd, so if you didn't like these ideas I'd be happy to suggest other ones as well. If you did like them, and have any questions, I'd be more than happy to answer. Thanks, hope these helped.
(I also just realized this thread was from 20 days ago. Hopefully I'm still on time to help.)