No, the Bristol Channel does not separate Great Britain from mainland Europe.
The Bristol Channel is a large inlet separating South Wales from South West England (Devon, Cornwall, Somerset). It connects to the Celtic Sea and Atlantic Ocean.
The English Channel (La Manche) is the body of water between southern England and northern France—it separates the island of Great Britain from continental Europe.
Key difference: Bristol Channel is within the UK; English Channel is between UK and Europe.