What motivated the British empire to build a global empire?

The answer is commerce.

The British Empire comprehended the domains, colonies, protectorates, and other territories under British rule, between the 16th and 20th centuries. The British Empire was the first global Empire in History because they built a global trade network based on their domain of the seas and the scientific and technological advances of the modern era. The British government intelligently boosted the commercial networks and the discoveries of new lands in order to get resources for the new industries that were created in the United Kingdom during the 18th and 19th centuries. In order to supply this new industrial market with the needed natural resources, the British crown adopted an aggressive foreign policy to extend its power and grant access to the sources of money and raw materials.