This isn't going to be much help, but beer retailing quite often went with blacksmithing, people waiting for a horse to be shod were something of a captive market. Common names for pubs associate with a blacksmith were Jolly Blacksmith, Blacksmith's Arms, Three Horseshoes ...
There was a Bald Faced Stag in North Road, Finchley, in 1874, licensee a Wm F Pickering. Earlier than that, there might be some information in trade directories or Quarter Sessions records. The name couldn't be Bates could it, just seems a bit more likely than Bafe.
Robert