There are geographical and historical reasons for the lack of British colonies in what would become the Western United States.
The primary reason why the Western United States did not have British colonies was because of geography. The European nations who sent colonizing expeditions around the world have coastlines on the Atlantic Ocean. These nations then claimed the areas of the Americas adjacent to the Atlantic Ocean. For example, Portugal's colonies in South America were on the eastern coast (e.g., Brazil). Similarly, England's colonies were on the Eastern seaboard of North America; it was difficult for England to establish a presence in the Western United States because it was difficult to access by sea.
There are also historical reasons for England's failure to colonize the Western United States. Much of what became the Western US was claimed by Spain, not England. Additionally, the West was settled long after the American colonies gained independence from England (between 1776 and 1789). The Lewis and Clark expedition in the early nineteenth century helped establish America's claim to what became the northwestern part of the United States.
For these reasons, Britain was never able to establish colonies in this area.