Free trade as viewed in the question (as we understand it today):
I understood Free Trade to mean the idea that trade between nations should not taxed or restricted, and that in the long run free markets operate to the benefit of all.
Free trade in the context of colonisation:
Free trade imperialism was a nineteenth-century English political movement that advocated a primary focus on commercial domination, rather than formal colonization and territorial expansion. Over time, the phrase came to refer to the use of military and diplomatic power to force underdeveloped, or militarily weaker, countries to grant access to their markets to more powerful states.
Under the Wikipedia entry of 'New Imperialism' -- on why Britain needed to do this (emphasis mine):
In historical contexts, New Imperialism characterises a period of colonial expansion by European powers, the United States, and Japan during the late 19th and early 20th centuries. The period featured an unprecedented pursuit of overseas territorial acquisitions. At the time, states focused on building their empires with new technological advances and developments, making their territory bigger through conquest, and exploiting their resources. ... The American Revolution (1775–83) and the collapse of the Spanish Empire in Latin America around 1820 ended the first era of European imperialism. Especially in Great Britain these revolutions helped show the deficiencies of mercantilism, the doctrine of economic competition for finite wealth which had supported earlier imperial expansion. In 1846, the Corn Laws were repealed and manufacturers gained, as the regulations enforced by the Corn Laws had slowed their businesses. With the repeal in place, the manufacturers were then able to trade more freely. Thus, Britain began to adopt the concept of free trade.
A lot more historical details available in a useful 1999 article on this very point, "British Free Trade, 1850-1914 - Economics and History" (pdf) by the The Economic History Review - http://www.ehs.org.uk/
At page 2, under British free trade, foreign economic policy and imperialism, this would be closer to your question:
The treaty system was always subject to critical attack from a number of quarters. Some politicians and officials stuck to the belief that free imports were the key to prosperity and that negotiation was not only unnecessary but also undignified. ... A large part of the problem was due to Britain's limited ability to bargain because she had already abolished most of her tariffs. Because the few tariffs retained were designed to raise revenue for the state they could not be cut much without seriously threatening the state's income and raising the spectre of increased domestic taxation.
On page 4 of article, relevant passage is (the impetus for expansion):
Free trade imperialism remained an important element in British imperial expansion in the 1880s and 1890s. As tariffs rose on the continent, British businessmen became increasingly interested in compensating themselves for lost European markets by vigorously supporting imperial expansion in Africa and Asia, thus preventing France and Germany from establishing protectionist regimes in those places where future economic prospects looked most favourable.
From a political-economic perspective (of why one state might colonise another), the answers are essentially more manpower and international market access. Here's an explanation:
For over two millennia, historians and philosophers have asked why some nations have expanded, why others have contracted, and what is the optimal size of a polity (Plato, for example, said that the optimal size was 5,040 families). ... The most important are economies of scale in production and military power. When barriers to free trade exist between countries, a more populous country achieves greater economies of scale through its larger domestic market. A larger population also allows for greater military power, which may make war against smaller and weaker states more profitable because of the higher probability of success. At the same time greater military power makes predation by other states less profitable to these other states and therefore less likely ... When barriers to free trade are reduced (so that economies of scale can be achieved within a small country as long as it has sufficient international sales) and the returns to warfare are decreased, the number of countries will increase and the average country size will decrease. The returns to warfare depend greatly on the nature of the victim country’s wealth. If the wealth is in oil, the predating county can expropriate most of the wealth ...
Source: The Oxford Handbook of Political Economy (2006), pp.39-40.