That is the holders of the formal title of Legatus Augusti Pro-Praetore Britannia.
In the year 43 AD a force of some 50,000 men under the command of Aulus Plautius landed at Rochester in Kent, defeated the British at the battle of the Medway, captured Camulodonum and established the Roman province of Britannia. The first Governor of Britannia was naturally enough Aulus Plautius himself although the province he governed was geographically limited to what we would now think of as southern England and consisted largely of the former territories of the Catuvellauni tribe.
His immediate successors seemed concerned with consolidating their hold on the new province, coping with the threat posed by the tribes of the Silures and Ordovices on the western frontier (and the stubborn resistence of one Caratacus) as well as maintaining good relations with the client state of the Brigantes that protected the northern frontier.
It was Gaius Suetonius Paulinus who had to cope with the Boudiccan Revolt in the year 60 AD which posed a signficiant threat to Roman dominion and almost succeeded in driving the Romans out of Britain.
Once that storm had passed, the province expanded northwards, and under Quintus Petillius Cerialis grew to include the territory of the Brigantian tribal federation north of the Humber. It was his successor Sextus Julius Frontinus who subdued the Silures of southern Wales who in turn was followed by Cnaeus Julius Agricola who conquered the Ordovices of northern Wales, took the island of Mona and pushed the northern frontier of the province beyond the the boundaries of the Forth and Clyde to the edge of highlands.
The threat posed by the revolt on the Danube in 87 AD forced the Romans to withdraw the Legio II Adiutrix and this reduction from four to three in the number of legions stationed on the island of Britain signalled an end of the expansionist phase in the Roman occupation. Ideas of subjugating the northern tribes were abandoned, walls were built and abandoned, forts built and garrisoned as the Romans concentrated on defending what they had acquired.
Our knowledge of Roman Britain depends largely on the survival of contemorary records; these are relatively detailed for the first century AD with the exciting business of Britain was being conquered, but became sparser thereafter as Britannia become a provincial backwater. There are often therefore gaps in our knowledge as well as periods of disruption and civil war when there may well have been no one whatsoever holding the formal title of governor.
Publius Helvius Pertinax for example briefly became emperor after the murder of Commodus on the New Year's Day of 193 and lasted three months, Decimus Clodius Albinus was also proclaimed Caesar after the death of Pertinax, and therefore technically was an Emperor not Governor until his final defeat and death in 197 when Septimius Severus appointed his successor.
The list ends at the beginning of the third century for the simple reason that in the year 216 the emperor Septimius Severus decided to divide Britain into two provinces; Britannia Superior, comprising the south and west, and Britannia Inferior the north of the country.