Britain lost interest in its North American colonies in the mid-1800s. The colonies were too expensive to maintain and defend. Also, they were not creating much profit selling lumber and other goods. This, along with other factors, lead to the Canadian Confederation. So, I was wondering, in Britain, which colonies did the government find profitable or desirable? Also, how did the public think of the colonies? Did they agree with the government's preferred colonies? If not, which colonies did they want to keep? I suppose it would also be nice to know which colonies did not become favourable in Britain's eyes. Oh, and I should mention I am referring to British colonies, not those of other European powers.
The first part of your question is fairly simple so I hope it will be fine if I don't include sources... In terms of the Americas, the most profitable colonies were the Caribbean colonies. These small islands produced vast amounts of crops, generally sugar cane, using slave labor, and were the most profitable especially for their size. Notably, Barbados, the Bahamas, and, to a lesser extent, Jamaica were all very valuable and produced a lot of trade goods. Trade winds also favor the Caribbean, further assisting trade. Overall though, India was the most profitable colony for the United Kingdom. It was known as the 'Jewel in the Crown' of the British Empire. It produced a wide variety of goods, ranging from tea to spices to opium. India alone produced plenty of products that helped give England global trade dominance. However, the British did not really gain dominance in the region until the 18th and 19th centuries while the Caribbean was colonized in the 16th and 17th, so it really depends which period of English history you want to look at to determine which was the most valuable.