No Roman armies returned to Britain after Caesar's second foray there in 54 BCE. It is possible that Caesar intended to return, but I doubt it, and he became distracted by the Treveri and then Vercingetorix in the meantime, and then the Civil War. Britain became a footnote, an unimportant and remote corner of the world in a veritable ocean of conquered territories in the 50s BCE--at least to Roman armies and generals. For the most part, this means that Britain disappears from literary sources as well, save for some vague, fantastical references in the Augustan poets (especially Horace).

As you suspect, contact between Britain and the Continent did not cease after 54. It was, however, severely reduced, as archaeology at British Channel port sites indicates, especially Hengistbury. The quantity and contents of visible trade (mainly amphorae for wine) drops significantly from the pre-Caesar to post-Caesar period in Britain. This is no doubt largely due to the impact of Caesar's actions themselves. In the two years leading up to his first "invasion" in 55 BCE, Caesar defeated the Amorican and Venetian peoples, both of whom maintained a sizable cross-channel presence. The destruction of the Veneti and their fleets probably severely curtained the amount of general maritime traffic across the Channel in the decades after Caesar's visits, simply because the war in Gaul had decimated the Continental elite and their access to the wealth needed to rebuild shipping fleets. Caesar's interventions also changed the political situation in Britain, especially around the Thames estuary, which took a few decades to "fall out."

The result of these shifts in the regional flow are seen in the shift of focus, in southeastern Britain, away from the old entrepot at Hengistbury and to a new, pro-Roman(?) port at Poole harbor. There were probably new or renewed port facilities at places like Southhampton Water and Chichester as well, though the Thames estuary seems to have become the preferred nexus for trade with the Continent by the end of the 1st century BCE, either because of Roman favor there or because of political jostling within Britain's tribes.

You ask about the identities of the traders. Our sources say nothing about this, but that is not surprising, since our sources rarely if ever mention the droves of "Italian" (now Roman) merchants which crisscrossed Rome's new territories long after the armies had departed. Wherever there was money to be made, mining speculation to be carried out, slave markets to be established, agricultural produce to be exploited, Roman merchants could be expected to be there, making deals. It is no different for Britain in the late 1st century. In the decades after Caesar's conquest, roads snaked out from Lugdunum (Lyons) in Gaul to the Continental channel ports. While roads are generally understood to be primarily for the movement of soldiers, and secondarily for economic ventures, in this case it seems fairly clear that these roads were at least partially the result of a certain amount of integration occurring between SE Britain, the rapidly-organizing interior of Gaul, and the Roman markets of the Mediterranean beyond. We know that enclaves of Roman merchants existed in Gaul before Caesar's time there, specifically at emerging Gallic towns (oppida) like Cabillonum (see Caes BG 7.40-42). We find a similar "enclave" of people who seem to be Roman in Britain at a spot in East Hertfordshire. There have been found: amphora for Italian wine and olive oil; vessels for fish sauce (a Roman calling-card); North Italian tableware; luxurious glass wares; a plethora of bronze toilet and medical implements; and writing implements and some Latin graffiti. None of these things positively confirm Roman presence, but all of them together is pretty good evidence. These would then be the Roman merchants, the negotiatores, who were busy setting up economic advantage under the auspices of Caesar's tenuous agreements ahead of their competitors. There were almost certainly similar enclaves at places like (what would become) Londinium and Camulodunum (later Colchester).

Gauls were not excluded as middlemen, however, as the archaeology clearly supports. In general, the "Estuary Zone" (e.g. places like Kent and Hertfordshire) start showing signs of paradigm shift in their material culture in the post-Caesarian decades. Most famously, we find a lot of new cremation burials accompanied by fine, wheel-turned pottery. Both of these things are strongly associated with 1st-century Gallo-Belgic practice, not British practice. This emerging shift in SE Britain is termed the Aylesford-Swarling culture. Changes like this can indicate several, overlapping phenomena: first, they show that contacts between the Isle and the Continent were not cut off in Caesar's wake; on the contrary, the exchanges we know to have been happening before Caesar obviously continue, even though our other evidence suggests the volume of trade had decreased due to Caesar's interruptions. Changes in burial rites also often indicate a change in the practices of the elite, who are the ones who usually have graves elaborate enough to survive. Changes in the elite practices were also going on in Gaul in this time period as the Gallic aristocracy was "becoming Roman" (see Greg Woolf's book on this subject). "Romanization" often begins with the elite. We can surmise that the native elites on both sides of the channel were maintaining or strengthening connections (not necessarily friendly), competing with one another, copying one another, and that Roman input was present for both, or else in a continuum of Roman -> Gallic -> British.

Some archaeological finds in Britain dating to the period 50 BCE to 50 CE (roughly) also indicate early integration of Britain into the larger Mediterranean network. Italian bronze and silver wares, like cups and jugs; ivory-embellished furniture; one grave even famously contained a pendant with the image of Augustus on it. All of this stuff could have been used in reciprocal exchanges between elites (gifts), but at the very least it indicates that Britain was not isolated and forgotten between Caesar and Claudius. Things were happening there, connections were being made, the British were being changed, molded by these contacts, and British elites were beginning to be connected to the larger world of Romanized elites, either via Romans themselves or through newly-minted Gallo-Romans. You mentioned in your OP that various client states were in contact with Rome in the time period, and this is true. This too suggests more connection between the Isles and Italy than is supported by the scattered and distracted sources.

Some places to go:

Creighton, Coins and Power in Late Iron Age Britain (Cambridge 2000).

Cunliffe, "Britain, the Veneti, and beyond" (Oxford Journal of Archaeology 1, 39-68)

Cunliffe, "Relations between Britain and Gaul in the first century BC and the early first century AD," in Cross-Channel Trade eds Macready and Thompson (1984).

Cunliffe, Hengistbury Head, Dorset various vols (Oxford 1987)

Cunliffe, Iron Age Communities in Britain (London 1991)

Cunliffe and Jersey, Amorica and Britain: Cross-Channel Relationships in the Late First Millennium BC (Oxford 1997).