Final answer:
The blending of British culture with the cultures in the English colonies, resulting in combined traits, is called syncretism.
Step-by-step explanation:
When the English established colonies in foreign areas and the cultures of those areas began to adopt some characteristics of British culture while retaining some features of the original culture, the term that best describes this process is syncretism. Syncretism refers to the blending of different cultural elements or religious practices into a new system, often seen when distinct cultures interact and combine elements from each. This is distinct from assimilation, which is the process where a minority individual or group loses its own identity by taking on the characteristics of the dominant culture, often resulting in the loss of the original cultural traits.