Two different languages, two different purposes.
One is for living and working in the UK, becoming a surgeon, etc, etc.
The other is for 75m+ people in 15 countries who need to communicate with others who between them speak over 500 languages and multiple dialects.
PS - if people only spoke West African Pidgin, that would make it a Creole, not a Pidgin. Or is it just that their first/second/third languages don't count in your mind?