This is a very interesting question! I would love it if an expert on British imperialism or trade policy would also comment to provide more context on British investment in South America. In the meantime, after rereading your question and the backstory you provided several times, I came to the conclusion that both of you are actually right.

I think that your history teacher acquaintance must have been objecting to the revisionist notion that Great Britain encouraged the war by turning Brazil, Argentina, and Uruguay into capitalist war machines, so that Britain could force its way into Paraguayan markets to turn big profits. Casting the Paraguayan War through the lens of the “dependency theory” represented a big push among historians during the 60s and 70s, and one still sees the remnants of the debate now and then in nationalist histories. Over the last thirty years though, at least among prominent North American historians and major historical publications, historians have largely rejected this thesis in favor of an explanation of the war as a consequence of state-formation and economic change of the mid-nineteenth century (check out a couple of my past explanations of this historiographic trend here and here).

Of course, Great Britain was heavily involved in South American affairs throughout the twentieth century, so much so that some historians (like the pioneering article “The Imperialism of Free Trade” by Robinson and Gallagher) argued Brazil and the Río de la Plata were examples of informal empire, though this has been significantly debated (see Knight, “Rethinking British Informal Empire in Latin America (Especially Argentina);” Rock, “The British in Argentina: From Informal Empire to Postcolonialism;” De la Escosura, “Lost Decades? Economic Performance in Post-Independence Latin America”). As you well know, prior to the war, Britain was rapidly ascending to international economic dominance, and thus, it should come as no surprise that British economic investment was extensive among all four of the combatants. During the first half of the nineteenth century, British capital investment in the region, though the largest of any nation, remained comparatively small for a variety of reasons (e.g. There was only a modest market for British industrial goods; political instability and conflict made investment extremely risky; infrastructure was basically nonexistent). Nonetheless, Britain profited from access to raw materials and foodstuffs from the nations that would one day constitute the allies. On the other hand, very little British investment reached Paraguay due to Francia’s policy of isolation and Argentina’s refusal to recognize Paraguayan independence. Furthermore, Paraguay had little to offer British investors as it lacked both raw materials and a sizeable market.

From 1850 on, British investment in the region surged. Stabilizing nation-states, further industrialization, and new investment opportunities in infrastructure and public utilities allowed British investment like never before. British capital markets also overcame fears of defaults to offer loans to the governments of the developing countries. Paraguay opened up as well, modestly industrializing with the help of a small British immigrant community. This included arms shipments and technical support, though diplomats in Paraguay discouraged Paraguay from getting involved in conflicts with its neighbors.

Yet, as John Dawkins points out in his article “Imperialism and the Victorians,” “British influence worked almost entirely through private interests and enterprise, with at best spasmodic intervention by diplomats and cruisers” (617). The interventions that did occur usually started in an effort keep waterways open or support British community or financial needs. In reality, the government never had a cohesive policy of involvement in the region that favored one country over the others. Instead, British investment and trade existed mostly along private channels in all four of the nations that would take part in the war.

This policy of official neutrality continued once war broke out. Due to its landlocked location at the center of the continent, Paraguay was almost immediately cut off from the outside world because of the Brazilian blockade of the Paraná/Paraguay river system. This essentially closed the door to arms shipments or capital loan deals, a key development that hindered the Paraguayan war effort. As the war progressed, British banks offered loans to Brazil and Argentina through bond markets, though these were modest and had little enthusiasm among bond buyers. Additionally, Brazil and Argentina had access to arms and naval shipments that over the course of the war negated Paraguay’s earlier military equipment advantages.

So British involvement before and during the conflict orbited around the notion of neutrality and private profit rather than significant British support for one side or the other. There does not seem to be evidence that Britain switched sides during the war because they knew Paraguay was going to lose; instead, Britain supported the allies more during the war due to geographic realities.

One last caveat: Among North American historians that I have read, few mention British involvement in the war at all because it was comparatively small to other economic situations occurring in other parts of the world during the 1860s; I usually come across the debate about Britain’s role in the war among South American historians. I assume that this is due to the patriotism and nationalism that still surrounds the war and its consequences. Personally, I find the explanation of the war as an expression of state-formation to be a more satisfying context of the war that gives agency to those who precipitated the conflict and a more fitting honor to those who gave their lives as a result.