This is a really cool website that lets you take a look at travel times and distances through out the Roman world depending on the mode of transportation, speed at which it moves, seasons, etc.
No-one has addressed this yet, but you probably wouldn't be doing this in 600! By then the integrated empire-wide trade network had broken down and although long-distance exchange still happened, it was limited to wealthy coastal cities that retained a powerful elite. It is difficult to find archaeological evidence for grain, but low-quality pottery by this point had very local distribution patterns, so we can assume that other non-luxury goods, like grain, were likewise only limited to local markets. In any case, sending grain was probably not feasible or economically justifiable even in an earlier period. As for how Rome was fed in late antiquity, its breadbasket around 600 was Sicily and we have letters from Pope Gregory the Great (590-604) detailing his work sorting out the logistics of getting food from there to the city. North Africa was still very productive as well and perhaps another source of grain; at the very least, we know that Sicily and North Africa kept the Roman empire financially afloat once it had lost the economically vital province of Egypt in 642.
There was trade between the Mediterranean world and England, but it had fallen off as the sixth century went on, perhaps because of the Justinianic plague that swept across the late antique world from the 540s onwards (one hilarious suggestion I've read is that eastern traders brought the plague to Cornwall and killed off their customers, awkward!) or for more mundane reasons of political unrest, economic decline, and cultural change. Intriguingly, we do have an eastern source from the early 640s, Leontius of Neapolis' hagiography of John the Almsgiver, the patriarch of Alexandria from 610 to 620, which explicitly mentioned a sea-voyage from Egypt to Cornwall and back. The story goes like this:
He [the patriarch] immediately ordered that one of the ships belonging to the Holy Church of which he was head should be handed over to the captain, a swift sailer laden with twenty thousand bushels of corn. The captain, when he had received the ship, sailed away from Alexandria, and on his return he made a solemn statement to the following effect: 'We sailed for twenty days and nights, and owing to a violent wind we were unable to tell in what direction we were going either by the stars or by the coast. But the only thing we knew was that the steersman saw the Patriarch by his side holding the tiller and saying to him: "Fear not! You are sailing quite right."
Then after the twentieth day we caught sight of the islands of Britain, and when we had landed we found a great famine raging there. Accordingly when we told the chief man of the town that we were laden with corn, he said, "God has brought you at the right moment. Choose as you wish, either one 'nomisma' for each bushel or a return freight of tin". And we chose half of each.' Then the story goes on to tell of a matter which to those who are ignorant of God's free gifts is either hard to believe or quite incredible, but to those who have experienced His marvelous works it is both credible and acceptable. 'Then we set sail again,' said the captain, 'and joyfully made once more for Alexandria, putting in on our way at Pentapolis.' The captain then took out some of the tin to sell - for he had an old business-friend there who asked for some-and he gave him a bag of about fifty pounds. The latter, wishing to sample it to see if it was of good quality, poured some into a brazier and found that it was silver of the finest quality. He thought that the captain was tempting him, so carried the bag to him and said, 'May God forgive you! Have you ever found me deceiving you that you tempt me by giving me silver instead of tin?'
The captain was dumbfounded by his words and replied: 'Believe me, I thought it was tin! But if He who turned the water into wine has turned my tin into silver in answer to the Patriarch's prayers, that is nothing strange. However, that you may be satisfied, come down to the ship with me and look at the rest of the mass from which I gave you some.' So they went and discovered that the tin had been turned into the finest silver.
We have no way of proving this journey ever happened, so it's perhaps best to only treat it as a topoi-driven narrative written to heap praise on the patriarch, but it is nonetheless the only description of a sea-journey from the Mediterranean to England or vice versa, so it is an important source to consider. It also implies that this kind of trade was the exception, since the ship only got to Cornwall because of a freakish wind. Archaeologically speaking luxury goods were simply not moving from the eastern Mediterranean to the British Isles, so presumably less profitable goods had even less of a chance of being passed along by trade. If you were an aspiring merchant, you most likely would not have taken the risk of sending grain to Rome in such a fashion! People did continue to travel for other reasons, but it would have been by land, at least through Gaul/Francia, before you got on a ship at Marseilles to sail to Italy, based on the descriptions of how the missionaries who went to England from Rome and the Anglo-Saxon pilgrims who went to Italy traveled across the Continent.
This isn't strictly what you wanted, but it should give you a sense of why trade would have been very difficult in this period. Trade was rare, not due to tolls or state-imposed policies, but because of the lack of a strong state that bound its regions together through its high expenditure (mostly on the army and the grain trade). The fact that we only have one source for such a trading expedition says it all really. In the Mediterranean world, we have many more sources attesting to ships sailing back and forth in the seventh century, but England was firmly on its distant periphery and seemingly disconnected from this network.
Why would you want to ship grain from Britain? Apart from the fact that you wouldn't be shipping grain to Italy at all in 100, B.C., when Britain was an outlying part of the world barely known to the Mediterranean, or 600, A.D., when the grain trade to Italy from the provinces had long since ended, the cost of shipping grain from Britain wouldn't have been worth the reward. Britain was not a major producer of grain, and the grain they produced was mostly spelt, which was not usually eaten in the Mediterranean--we have references to it, but only a few. The Mediterranean produced vastly more grain than Britain could ever dream of. Sicily alone provided Italy with a tenth of her grain harvest in tribute each year, amounting to 3 million modii, and in times of crisis the Romans generally bought more. Africa, according to Josephus, could feed Italy for 8 months every year. Egypt provided, according to Pseudo-Aurelius Victor, 200 million modii per year during Augustus' reign! Anything that Britain could've provided was insignificant and not worth the cost of shipping it all the way into the Mediterranean. Most economic activity in Britain remained in Britain. Agriculture was the most important part of the economy of the province, along with pottery and other crafts, but the OCD notes that Britain didn't really export much to the other provinces besides precious metals, which were in abundance, with the majority of its economic activity remaining in the province.
Anyway, if you really wanted to ship grain from Britain for some reason, despite the fact that you'd probably lose money on the venture or at least not make enough to justify the pain in the ass it would cause you, you'd do it through what are called navicularii. Navicularii were private ship owners, and unless you happened to own a ship yourself you hired out one of these guys. They were pretty common in the Mediterranean, where everything was shipped by sea even over very short distances (it was actually cheaper, for example, to ship grain from Sicily by sea to Rome than to ship by land from Apulia), and they were often freedmen--Trimalchio in the Satyricon claimed to have made his fortune as a navicularius. During the Principate these private ship owners could transport whatever they wanted, and usually did, but they were given special exemptions and privileges if they spent at least some of their time transporting grain. After Claudius navicularii who hauled grain were reimbursed by the state if their cargo was lost in a storm, and were granted special legal privileges--citizens who hired out their ships for the grain trade were considered exempt from the lex Papia Poppaea (one of Augustus' laws on marriage which, among other things, prohibited marriage between a senator's daughter and a freedman. It's easy to see why this would be popular among the freedman-dominated navicularii), Latins who did so were given citizenship, and women were granted the many privileges of those who bore four children. In late antiquity it was actually made a civic duty to haul grain to Italy, probably just for navicularii in the Mediterranean since little to no grain was transported from northern Gaul or Britain. These navicularii seem to have mostly operated through middlemen who ran the great granaries (horrea) that we find at port cities throughout the Mediterranean. Usually farmers did not sell their grain directly for export. Most grain that was shipped was shipped by the provincial governor (or in the Principate the procurator) as part of the grain tax, who would collect the tax and sell it to the guys at the horrea, who would then sell it to navicularii to ship out. This seems to be basically the practice going back to the Republic. We know, for example, that the provincial governor of Sicily could buy or commandeer additional grain besides the tenth provided by the grain tax, and that unscrupulous governors often got rich by selling this extra grain. Governors could also requisition grain for their armies--Piso was accused by Cicero of requisitioning more grain than he needed and selling the excess. So this indicates that there was some sort of chain of middlemen and that grain wasn't just dropped right on the navicularii straight from the governor. I've never heard of farmers selling their grain for export privately, besides what they provided for the grain tax, but I suppose it's not impossible, and we certainly lack a lot of sources about the lives of provincial farmers.
Finally, there were in fact import duties. The vectigalia were a class of imposts and taxes on various transactions, especially rents paid on the ager publicus, trade duties, slave sales and manumissions, and (during the Principate) property left behind in wills. The most important of the vectigals were the portoria, fees on goods entering or leaving harbor. Originally the portoria were only levied in Italy, although they were suspended briefly during the 50s, B.C.--Caesar re-established them during his dictatorship. This later extended to provincial ports and then to cities on land trade routes, although trade in the Roman world occurred by sea whenever possible. These aren't really import/export fees, though, because this is domestic trade. The fee on such trade was generally around 2.5%, as it was in Gaul and at Ephesus, whereas goods entering a province from outside the empire were assessed at a much higher rate--the OCD says that the fees on goods entering the eastern provinces from outside the empire were fixed at 25%!
It's worth noting that there was no 'England' in 100 AD, as the Angles didn't settle in Britain until approximately 400 years later, and even then a unified 'England' didn't exist for several centuries after that until the 10th century. The Romans called the area Britannia.