The traditional answer is 410 CE, but the issue is rather cloudy. Roman Britain had been attacked time and again by Saxon pirates, and in 407 CE the usurper Constantine III led the Roman forces in Britain to Gaul with him in part of his attempted rebellion. In the Emperor Honorius, realizing that Britain was untenable and that there was no force he could send to garrison Britain, sent a message calling for the evacuation of Britain and telling the locals that "You must now look to your own defenses." It becomes very unclear what happened over the next 200 years in Britain as a clear narrative, as our clearest source, Gildas' "On the Ruin and Conquest of Britain," isn't very reliable at all, but it appears that the Romano-Britons (who would soon begin to be called "Welsh") resisted in some areas and submitted in others to Saxon invaders. It is very difficult to say when London proper fell to the Saxons, though Peter Heather's Empire and Barbarians argues that the Romano-British were likely holding their own at least into the 440s.

Empire and Barbarians is a good resource, but the topic is very, very cloudy.