Britain was a part of the Roman Empire from the first century BC on. Not only was the native Celtic population conquered by the Roman legions, but the conquerors settled down and established Roman culture. Cities were quickly established with forum and amphitheater and temples and baths, like the Roman provincial capitals on the Continent. Roman foods that had never been seen before in Britain were imported.
A lot of the imports were driven by the needs of the army. Although Britain was a fairly small part of the Empire in terms of square mileage, it originally garrisoned a great many soldiers as a frontier territory, with unconquered people still there in Cornwall and Wales and wild Picts up in Scotland. Hadrian's Wall (built under the emperor Hadrian) stretched across what is now northern England, designed to keep Picts out.
Wine and olive oil were imported for the armies--and adopted by the wealthy locals, who started adopting Roman ways. Apples and pears, dill and coriander, chickens and pigeons, cabbages and daffodils were established and eaten in Britain for the first time. (Yes, daffodils were eaten.) The legions built straight, paved roads to travel on and worshipped warrior gods at Roman-style temples.
By the third century AD the wealthy of the original local population had thoroughly adopted Roman culture. They built large, comfortable villas with mosaic tile floors and heated baths. Even now, digging in much of England will turn up a lot of flat Roman bricks. Even after the size of the stationed armies began to decline, as troops were needed off on the eastern frontier, and as imports dropped proportionately, the wealthy had local potteries produce tableware that looked a lot like what had once come in from the Continent. These Romanized Celts, however, turned back to beer and butter once wine and olive oil stopped arriving on Roman ships.
The fourth century saw two major changes. First, the Empire became Christianized, starting in the time of the emperor Constantine. Roman Britain also became Christian, and the old pagan religions, a mix of local deities and imported Roman gods, moved to the margins. By the middle of the fourth century Britain was so thoroughly Christianized that it even developed its own Christian heresy, Pelagianism, which essentially denied original sin and said that humans could avoid sin and create their own salvation without receiving (undeserved) grace.
Secondly, in the later fourth century most of the remaining Roman legions pulled out, to go fight in Persia or along the Danube. As they left, the Angles and Saxons showed up. These were Germanic peoples from what is now northern Germany (Saxony), who came across the North Sea and conquered, destroying much of Roman culture. If school textbooks still talk about the Roman Empire "falling" to Germanic peoples, it is because this actually did happen in Britain, even if not in most of the rest of the Empire, where the Germanic people tended to settle down and become Roman (as in Gaul/France and Spain).
Last-ditch fighting by the Romanized, Christianized population was led by a war-leader (dux) named Arcturus. He even was temporarily successful, enough that he became the King Arthur of much later legend (on which see more here). But shortly after 500 the Angles and Saxons triumphed. England is named for the Angles. At least some of the Christianized population fled to the margins, although others just accepted their new rulers.
For about a century Britain was cut off from the Continent. This time is called the Dark Ages by the British, because so little is known about it. But starting around the year 600 missionaries from Rome and missionaries from Ireland and Scotland began seeking to convert the pagan Anglo-Saxon kings, who had divided the island into a number of small kingdoms. The missionaries' efforts were helped by the fact that a lot of these kings had married Christian princesses from the Continent.
By 700, Anglo Saxon England had developed literacy (in both Latin and Anglo-Saxon), written law codes, and a sturdy Christianity. Yet its culture remained quite distinct from that of the Continent, where Roman culture persisted much more strongly, until the Norman Conquest of 1066.