Monmouth says that round about 1100 BC, a mythical Trojan named Brutus, descendant of the equally legendary Aeneas, brought a fleet of ships to Britain after many, many adventures. There were only a few giants living there at the time, and besides, the island had been promised him by a goddess, so he helped himself.
After that he had seen his kingdom, Brute was minded to build him a chief city, and following out his intention, he went round the whole circuit of the land in search of a fitting site. When he came to the river Thames, he walked along the banks till he found the very spot best suited to his purpose. He therefore founded his city there and called it New Troy, and by this name was it known for many ages thereafter, until at last, by corruption of the word, it came to be called Trinovantum.About a thousand years and many mythological kings later, just before the arrival of the Romans, Trinovantum was due for renovation.
Unto him (Hely) were born three sons, Lud, Cassibelaunus and Nennius, whereof the eldest born, Lud, to wit, took the kingdom on his father's death. Thereafter, for that a right glorious city-builder was he, he renewed the walls of Trinovantum, and girdled it around with innumerable towers. He did likewise enjoin the citizens that they should build houses and stately fabrics therein, so as that no city in far-off kingdoms should contain fairer palaces. He himself was a man of war, and bountiful in giving of feasts. And, albeit that he had many cities in his dominion, yet this did he love above all other, and therein did he sojourn the greater part of the whole year, whence it was afterward named Kaerlud, and after that, by corruption of the name, Kaerlondon. In a later day, by the changing of the tongues, it was called London, and yet later, after the landing of the foreign folk that did subdue the country unto themselves, hath it been called Londres. Alter the death of Lud, his body was buried in the foresaid city nigh unto that gate, which even yet is called Porthlud in British, but in Saxon Ludgate.The Truth about the founding of London:
Although there were people in Britain long before Geoffrey of Monmouth believed the Earth was even formed, London was founded by the Roman occupiers, soon after 54BC. They didn't do it because they wanted fancier palaces than the ones in any of the other places they'd conquered either. In fact, it seems they didn't systematically found a city at all (as they did in other places). They just strung a few pontoons across the river at the lowest possible crossing point, as a shortcut on their way to Colchester. There had been nothing much there before, but Londinium grew up in an organic way (as cities often do) around the north side of the bridge, with a smaller settlement on the south side, and eventually took over as the Romans' capital city in Britain.