Great Britain's economic policy, mercantilism, required that the country export more goods than it imported. For this to happen, Britain needed to maintain its status as the world's strongest industrial power. Britain did this by acquiring colonies overseas. It was motivated to do this because it needed new markets for its finished goods. The colonies could also be used to supply raw materials for manufacturing.
The trouble with the colonies is that after the British economy became prosperous, British nationals did not desire to move to these locations, which were in inhospitable climes. This is where the slave trade becomes a factor. Because the colonies were primarily established to provide particular cash crops, which required numerous workers, slaves were utilized to make them profitable. The slave trade itself was also a very lucrative endeavor. Due to the need to make colonies profitable to increase industrial trade, Britain was closely tied to the Atlantic slave market. So to answer the initial question, Britain's economic policy was probably not viable without the trade and use of slaves.