I'm a little confused by your question, because the title and the text suggest different things. You've kind of conflated "technological advances in 1400-1800 England" with "expansion of the Empire" and "new markets." There were some technological developments over that time that contributed to Britain's economic growth and ability to project power: metallurgy and weapons manufacture improved significantly, as did shipbuilding, as did cloth manufacture. I should stress, though, that these were not the kinds of game-changers that things like steamships and machine guns were in expanding the empire. The technological developments of the early modern period are part of a broad assemblage of imperial techniques that include mercantile policies to sponsor long-distance commerce, the "fiscal-military state" which made the United Kingdom probably the best-organized and best-managed state in Europe when it came to collecting taxes, borrowing money, and allocating resources for war. Having a growing cotton cloth manufacturing center in Lancashire did lead to some accelerating economic growth in the 18th century, but it was nowhere near as important for establishing a North American empire as, say, the ability to raise, train, equip, and dispatch significant numbers of soldiers and sailors.

If we look specifically at technologies related to food and agriculture in the period from 1400 to 1800, then my answer to whether food choices changed is mostly no. British agriculture did develop new techniques for crop rotation, and it did become substantially more productive in terms of both land and labor. But, most of the foods that they ate in 1800 were eaten in 1400 as well: wheat, barley, rye, and oats remained the main grains; peas and beans were common legumes; beef, mutton, and pork were the main meats; cheese and eggs, local fruits and vegetables, beer and so on rounded out the diets. In many cases, the processing was also the same: the stone mills used to grind grain into meal in 1400 would have been perfectly recognizable to a miller in 1800, even if a few mills in 1800 had steam engines attached to them. Beer in 1400 was probably brewed mainly at home, while by 1800 it was largely a commercial enterprise. The scale was different, but it's not like some invention radically changed the beer. The overall choices of food were pretty much the same. There were some New World crops that became significant over time, but only slowly; potatoes are the only clear example of this, but they were not an enormous part of the British diet in 1800. Still, they were a choice, so I suppose they count: Britons in 1400 had only the grains and legumes mentioned above for their main starches, while they could have chosen potatoes in 1800.

There are three significant exceptions: sugar, spices, and "drug foods" like coffee, tea, chocolate, and arguably tobacco. Spices were rare and expensive in late medieval Europe; hence, not only Columbus's voyage across the Atlantic, but also Portuguese commercial expansion into the Indian Ocean, and then especially Dutch expansion into the East Indies in the 17th century. The VOC (Dutch East India Company) captured many of Portugal's Indian Ocean forts and became by far the largest supplier of spices to Europe at that point. Two points are worth mentioning with respect to the British diet and your question. First is that technology probably is not the most important factor in making the Dutch empire in the 17th century. They didn't capture much territory, and in many cases they, like the Portuguese before them and the British after them, occupied fortified trading posts less because they were technologically superior to local societies, but because locals saw them as acceptable and useful trading partners. They did possess better ships than the Indian Ocean societies they encountered, and that helped. But, their weapons were only slightly better and not enough better to make their armies invincible. Far from it--for the most part, Europeans were unable to press territorial claims inland beyond the reach of the ships' cannons. Hence, they tended to remain in fortified outposts for trade. In the one case where Europeans did begin to really press inland, with the British in Bengal in the second half of the 18th century, it was probably more a matter of greater financial resources than technology. The British East India Company routinely hired Indian troops and bribed their political opponents.

The second point about spices is that it's not clear to me how much they actually affected food choices. Spices definitely became cheaper and we do see things like pepper, mace, nutmeg, cloves, ginger, allspice, and some others make their way into British recipes. The bulk of the food was the same, but they could and did manipulate the flavor somewhat.

The next big exception are the "drug foods," coffee, tea, chocolate, and tobacco. These were virtually or totally unknown in Britain before 1400, but fairly common if not universal by 1800. Coffee is originally from East Africa but was being cultivated on plantations in the Caribbean in the 18th century. Chocolate and tobacco are originally American, but were also adapted for the European diet and grown on plantations in the New World. Tea was highly sought after, and became an important part of the British diet starting in the 17th century and expanding a LOT in the 18th century; its origin is in Asia, but it could at this point only be acquired through trade. Europeans did not learn to cultivate themselves until the 19th century, when they set up plantations in India. I hesitate to attribute these changes to "technology," for the reasons I mentioned above. European conquests in the New World were largely the work of disease, not technology. Sure, having good ships helped, but it wasn't the decisive factor.

Finally, there's sugar. Sugar was first known to Europeans through the crusades, and Europeans quickly developed a serious sweet tooth. It was expensive to buy from Arab traders, and not available in great supply. And, it was difficult to cultivate: it grows practically nowhere in Europe, and the first places Europeans found where it was worthwhile to grow were the islands of the Atlantic--the Madeiras, and later the Cape Verde Islands. The Caribbean and Brazil, however, offered the perfect climate and as early as (I believe) the 1560s the Portuguese were growing sugar in Brazil. The other European nations followed, setting up sugar plantations throughout the Caribbean region. Now, here again, technology was hardly the decisive factor--unless you count the slave-plantation system as itself a technology. It did require novel forms of organization, and the creation of new techniques to supply large numbers of slaves. But, this was more a matter of innovating in commercial forms, rather than in material technologies.

Thus, imperial expansion and the creation of new markets were pretty important in beginning to change European diets by 1800, but overall material technology was not. Now, if you'd asked about 1900, that would be a different story, because across the 19th century there are a series of developments that really do change diets.

See Drummond and Wilbraham's The Englishman's Food for an overview of the British diet. On the development of New World sugar plantations and its affect on the British diet, Sidney Mintz's Sweetness and Power is the standard work.