Well the very first encounter occurred at a date unknown. Roman traders were common in Gaul prior to the Gallic wars and it seems likely that Romans and Britons first met through trade.

The first major encounter came in 54BC, almost immediately after the Roman conquest of Gaul when Julius Caesar led a military expedition to the British southern coast. Caesar's pretext was that the Britons had to be punished for aiding the Gauls during the Gallic wars, although it is likely that Caesar's real motivation was the propaganda value in being the first Roman to visit the isles in a public capacity and to explore for valuable natural resources. Caesar found few natural resources and the expedition was almost a disaster when a storm wrecked many of his ships. However, news of the expedition in Rome added to Caesar's immense fame and popularity. There was some fighting but nothing very significant. Caesar would return the next year with a larger expedition and do a more extensive campaign into England.

Sources: Caesar (2010) Adrian Goldsworthy