The saxons and other germanic tribes were able to settle in britain because
the people didn't fight back.
the roman army had been pulled back to defend rome.
no one lived there.

The correct answer is The Roman army had been pulled back to defend Rome.

Indeed, in 383 A.D. Roman General Magnus Maximus left Britain and entered Gaul. He was able to execute Roman Emperor Gratian who had lost the support of the Roman people and Roman elites. This left the northern and western parts or Roman Britain undefended and Germanic tribes, that had been raiding such areas for decades now had free reign to invade and pillage at will.

During the next decades the raids and invasions increased and there were sporadic minor Roman campaigns that changed nothing. In 410 A.D. the last Roman magistrates were expelled from Britain the Romano-Britons reverted to their pre-Roman culture and ways and organized themselves to fight the Germanic invaders. They did not succeed and only Wales was able to resist.