You'd think it would have been a loss, but it was actually a long term gain.

First, the British no longer had to worry about financing the administration and defense of what became the USA. As an independent Republic, Americans had to swallow those costs.

Second, the American South developed along lines that were complimentary to the British economy. In the late 18th century tobacco wasn't the cash crop it had been during the 17th and early 18th centuries. Most of the US at that time wasn't exactly ideal for the production of cane sugar either, which combined with a lack of expertise as well as the fact that sugar mills are incredibly labor intensive. In the 1790s a combination of technological innovation, the spread of cotton species ideal to the American South, and the fact that Saint Domingue dropped out of the Atlantic cotton market (Haitian Revolution) led to an explosion of cotton production. The Southern planters also pushed to keep the US federal government from imposing protectionist duties which would hurt its trade with Great Britain. Instead, they did everything possible to facilitate free trade as they were increasingly dependent on GB for manufactures and industrial goods of all kinds. The fact that the USA was an ex-colony also eased this process as old trading contacts could be utilized and there were less language barriers than normally exist for this kind of thing. The US was already a historical part of the British Atlantic economy.

Third, long term processes really started gathering steam around the world. In Britain, policies privatizing collective lands and protecting the nascent textile industry really made headway into old social relations and productive networks. Technological advancement and industrialization in GB finally allowed the Brits to stop being simply the merchant middlemen for superior Indian wares and instead start producing equivalent wares at lower prices. They even started cutting into Indian domestic markets, turning a historic textile exporter into a net importer by mid-century. As the American South directed more and more slaves to cotton cultivation they were able to satisfy the seemingly bottomless demand for cotton among British textile manufacturers. This, of course, was not entirely a bottomless trade, as evidence through the crash of 1837, rooted in the overproduction of cotton, but the gap between demand and production was wide for long enough to make it seem like a sure thing for American cotton producers and traders.

Fourth, whole new markets became available as decolonization in the Americas left both Brazil and Spanish America finally and fully open to British textiles. Indian markets were also increasingly penetrated and turned into dumping grounds for British textiles.

Even when the British went to war with France they were able to fall back on trade networks that they dominated, which overcompensated for losses from continental European protectionism and Napoleon's Continental System.

The strength and value of these ties between the American South and Great Britain as well as the weakness of a central power that couldn't override Southern interests within the legislature (in this case, couldn't impose protectionism that would disrupt US-GB trade in favor of American manufacturers)

During this period the US only briefly became a proverbial stone in their shoe, in the form of the War of 1812. The intense and mutually beneficial trade networks between both caused the conflict to be a parenthesis, rather than a turning point, in relations between the two.

The American South became key producer of primary goods for British trade and also a great market for British goods. British Capital vied with American Capital in financing slave plantations, which depended on credit for expansion or to compensate for bad crops or market conditions. What is more, American merchants were no longer a part of the British empire and thus didn't compete with metropolitan merchants within the British Atlantic economy.

Interesting reading on this subject:

Empire of Cotton by Sven Beckert.

The Modern World-System III: The Second Era of Great Expansion of the Capitalist World-Economy, 1730s-1840s by Immanuel Wallerstein.

The Cambridge Economic History of the United States, Vol. 2: The Long Nineteenth Century, Edited by Stanley Engerman and Robert Gallman.