Although the withdrawal and then collapse of the Western Roman Empire certainly put a dent in mercantile business, it was nowhere near ending it. There's a lot of dodgy pop history about how early Medieval England was basically cut off from Mediterranean trade, but it's all bollocks. As a theory among historians and archaeologists it died out in the later 20th century because we kept digging up all sorts of foreign goods at early medieval English sites, and the idea of England being cut off was not sustainable. The archaeological evidence is undeniable: the collapse of the Western Roman Empire did not lead to a catastrophic reduction in trade. To quote the paper "Early Medieval Trade Routes":

Virtually all historians agree that the Germanic invasions did not mark a turning point in the economic history of Europe though they may well have accelerated the decline and disintegration of the Roman Empire. Nevertheless, as soon as the first waves of these invaders had settled down in the new successor states, the Byzantine merchants revived western trade. A large portion of the evidence cited to support the persistence of the Roman pattern of Mediterranean trade... actually reflects this revival of commerce in the sixth and seventh centuries after the decline in the fifth.

In other words, while the Western Roman Empire was dying in the 5th century, trade dipped, but came back once the earliest barbarian kingdoms had been established.

Sutton Hoo is the most well known example of how goods continued to flow, but the focus on it sometimes leads people to think it was exceptional. Sure, the status of the grave and the value of the goods within is indeed remarkable, but the origins of those goods is not. We find Byzantine goods all over 5th and 6th century England, along with pottery from all over the Mediterranean world. We also find Byzantine (and later on, Arab) currency too, which the early medieval kingdoms often attempted to imitate in their own coins so that they could be used over long distances. This probably didn't work out too well - Arabian merchants may have questioned why gold coins from England have incorrect Arabic on them (or in the case of King Offa of Mercia's imitation dinars, pretty good Arabic that's upside-down) - but it demonstrates deliberate attempts to encourage long distance trade. This was so successful that many historians think the Byzantine Empire was actually running a trade deficit with the early medieval kingdoms, which may be why they debased their coinage for long distance trade from Justinian through Constantine IV Pogonatus. This policy ended with the Arab Conquests, when Byzantium also lost access to much of its gold and silver supply - then it was the Arab's turn to dominate trade currencies.

There was also the tin trade; some of the largest concentrations of Mediterranean goods outside of the wics come from the south-west of England, and from southern Wales. South-west England was known throughout the classical world for tin mines, and the departure of the Romans didn't mean people no longer needed tin.

But this continuation of long distance trade wasn't just an accident or natural development. Instead, it was deliberately fostered by early medieval rulers because they could tax trade pretty easily with customs duties. Early medieval rulers kept trade routes open by setting up emporia or wics, which were trade fairs designed to attract long distance traders, which due to a combination of that trade and a growing rural economy around them, often developed into wealthy cities. Some could be pretty large, and many of southern England's cities were either founded or revitalised as a wic. Some examples include Hamwic (Southampton) and Lundenwic (London). They were also common in Frankish and Carolingian France, as well as the Low Countries. These trade centres tended to be controlled directly by the king and organised into customs blocs, so merchants would pay duties to trade within one bloc, which got them access to a specific group of cities. They could be closed off or merged depending on trade relations between rulers (Charlemagne and Offa had a dispute that resulted in trade embargoes) and show that the early medieval rulers had a substantial interest in keeping old Roman trade routes going as well as fostering new ones. As the early Middle Ages continued, many wics were redesignated as 'ports of trade' where merchants could trade without having to pay certain taxes, or receive subsidies if they traded certain goods in specific locations.

So yes, England was very much wired in to the long distance trade networks of Europe, the Middle East, and beyond.

Sources:

Adelson, Howard L. "Early Medieval Trade Routes." The American Historical Review 65.2 (1960): 271-287.

Hemer, K. A., et al. "Evidence of early medieval trade and migration between Wales and the Mediterranean Sea region." Journal of Archaeological Science 40.5 (2013): 2352-2359.

Middleton, Neil. "Early medieval port customs, tolls and controls on foreign trade." Early Medieval Europe 13.4 (2005): 313-358.

Saunders, Tom. "Trade, towns and states: A reconsideration of early medieval economics." Norwegian Archaeological Review 28.1 (1995): 31-53.

Theuws, Frans. "River-based trade centres in early medieval northwestern Europe. Some ‘reactionary’thoughts." From one sea to another. Trading places in the European and Mediterranean Early Middle ages: Proceedings of the International Conference, Comacchio 27th-29th March 2009. 2009.