In the Middle Ages religion was not a major factor in drawing people to Britain. Sometimes the people who conquered England embraced the Christian religion that they learned about in England, like the Danes. Sometimes the people who came were already Christian, like the Normans, and they brought their own ideas about Christianity into England.
However people did travel in this period of history, both to go on pilgrimages to Christian sites in Europe and to fight in the Crusades. The church in Britain throughout the Middle Ages was Catholic and under authority of the Pope in Rome.
Although people of Europe spoke different languages and organised their cities and societies differently, ideas did flow through the continent. We know the Vikings travelled from northern Europe towards the east, founding the Rus empire, and then serving the Byzantine emperors in Constantinople.