The first British colony in west Africa to gain independence was

Ghana

Country in West Africa

On 6 March 1957, Ghana (formerly the Gold Coast) became the first sub-Saharan African country to gain its independence from European colonisation.

Ghana (Gold Coast) on 6 March 1957

Explanation:

After World War II the British colony of the Gold Coast in West Africa was the first British colony to achieve independence. To gain independence, some African leaders in the Gold Coast established a convention to demand greater participation in government.