There are no laws prohibiting dogs in pubs. (Some people regard having dogs in food service areas as possibly contravening food hygiene regulations but, once again, there's no specific legislation; having a dog in a food service area doesn't actually break any law).
Most of the big chains (e.g. J D Wetherspoon) ban dogs [other than registered assistance dogs] from their premises but, unless there's such a company policy in place, it's entirely up to the individual publican.