What is the difference between British language and English language?

The English language as it is written and spoken in Britain is called "British English." There is also an ancient British language, called Brythonic, which survives as Welsh and Breton.
The English language is the accepted standard language spoken at the time.

British language is the various colloquial languages spoken in Britain, there are over 200 distinct british dialects.

The standard is currently based on the Oxford English dictionary but is changing daily.