Custom and practice seems to favour the former. CAMRA's own newspaper, What's Brewing, uses that formulation, as does our Good Beer Guide. This organ, however, favours a capital T. My contention is that the The is an integral part of the pub name. You wouldn't say "I had a nice pint at Kingston Arms" or "fancy popping down White Horse". The name emblazoned on the side of a pub and on its pub sign invariably has a starting The.

Elsewhere in the world, we use a capital T where the The can't be disconnected e.g. The Times, Shakespeare's The Tempest. So why not pub names as well?

Cambridge being Cambridge, there must be someone out there who can provide a definitive answer.