Birmingham has never been the capital of London, England, or the United Kingdom.
London has been the capital city of England since the 12th century (superseding Winchester) and of the United Kingdom since 1707 (Acts of Union). It is a distinct city-region in Southeast England.
Birmingham is a major city in the West Midlands region, approximately 180 km (112 miles) northwest of London. It rose to prominence during the Industrial Revolution as the "Workshop of the World" and is now the UK's second-largest urban area. It has never held capital status.
Confusion may arise because Birmingham is often called the "Second City" (by population/economy) or because both are major metropolitan centers — but they are separate entities, 2+ hours apart by train.