London was to all intents and purposes founded by the Romans, when Claudius sent his legions to conquer the island of Brittania (as the Romans eventually called it). There may have been a native settlement there before, but it was almost certainly not called anything like London, nor did it have especial significance.
As Londinium it was the capital of the Roman province, until Brittania was sub-divided later. When the Romans left it appears to have carried on, for some time, because later records and archaeology point to a trading station just outside the western gates of the Roman city, at a suitable point for beaching ships. This later became known as the Ald-wich or "old city", when the Roman city was revisited by native kings, who doubtless found the semi-tumbled Roman walls useful.
Saxon kings ruled from here, when they weren't somewhere else in their kingdom, and William (the Bastard, of Normandy) built a Norman keep here which still exists as the White Tower within the Tower of London.
The main seat of government, however, migrated out of the commercial hub of London proper, upriver about 2 miles to the isle of Thorney where monks had built a cathedral, the West Minster. A hall was built here for the King, and around it grew the Palace of Westminster.