Short answer: Yes, they even met the Romans.

Long answer:

In Cunliffe, B. W. and de Jersey's Armorica and Britain: Cross-Channel Relationships in the Late First Millennium BC, it is stated that trade between Britons and European Gauls/Romans took place from the 2nd Century BC onwards. Their primary point of access was from what is now Hengistbury Head, Dorset; Cunliffe makes it clear in his 'Guide to Roman Britain' that this was the major trading centre between Europe and Britain. This is clear from the fact that more amphoras of Italian wine have been found here than in any other British site. The fact that most of these vessels date to before 50 B.C. is explained by how Caesar's invasion was actually bad for business in two ways. Firstly, as Britain and Gaul were major trading partners, Caesar's occupation of Gaul decreased trade. Secondly, after Caesar occupied Brittany and later the British Isles, trade was further diminished.

As for how aware they were about Europe as a continent, they certainly had knowledge of many different factions. According to Sills in 'Gaulish and Early British Coinage', trade agreements were negotiated by North French tribes in which they patronised British businesses in exchange for British aid in the war against the Romans. Britons also made extensive contact with the Belgic tribes of Northern France, as large numbers of Gallo-Belgic gold coins dating from circa 200 BC to 50 BC were all excavated in Southwest England (Cunliffe). These facts show that Britons did not only trade with Europeans in commodities, but also in diplomacy and currency.

But how much did they know about life (society/culture) outside the Isles? According to Cunliffe - I feel uncomfortable quoting so widely from him, but he really is the ultimate authority on late Iron Age Britain - burial customs in south-east England even changed to better resemble Belgic rituals. Julius Caesar in his Gallic War goes one step further, asserting that the Belgics were a part of the Britons, because they made raids on the Isles and settled there. There are also instances of rich men who were buried in their graves with Roman luxury objects, indicating that Roman culture and aesthetic standards had permeated British society. This is supported by DW Harding in 'The Iron Age in Lowland Britain', in which he lists many archaeological discoveries that suggest prolonged (from before 100 BC) interactions and trade between the Isles and the Continent. For example, gold tarcs in the Belgic style have been dug up in what is now known as Sussex.

The Britons also fought with some European 'invaders' before the Romans. The Catuvellauni were the 'native Britons'; the Dobunni and even the Iceni were considered mainland (mostly Belgic) invaders. According to Allen, prior to Roman occupation, there was an extensive tribal clash between these factions which ended anywhere around 100 - 80 BC. Nevertheless, not much is known about how everyday Britons felt about Belgics/Romans on a personal level, because of the lack of British writers whose works have survived.

In conclusion, it's clear that Britons had an extremely complex relationship with different sorts of Europeans, and that their interactions included trade, rivalry, and diplomacy. Hence, yes, it would be fair to say that they did know 'where the Romans were coming from', and that they knew much about their continental neighbours. There is however no evidence to suggest that the Britons ever led an exploratory mission to Europe, so they may have relied on word-of-mouth knowledge transmitted by traders.