As for the HB, it will certainly feel less authentic to me now that it's not filled with smoke, but my lungs will thank me and it will be nice to not have a separate jacket just for wearing there so it can smell smoky.
Given that England banned smoking in all pubs 18 months ago, one could argue that the HB is now more authentic. All it lacks is a eighteen-year-old chav passed out in the street outside the door with a traffic cone on his head. Oh, and hourly renditions of "American Pie" by the boozy mob within.
It won't be an authentic British pub until they have Carlsberg or Kronenberg on tap. Two beers that are on tap in almost every hole in the the wall in the UK, yet the only time I've seen them on tap in the US is at Streets of London in Sacramento (the best British or Irish pub I've ever been to). Ironically, neither is British but they're a staple in the pubs. Oddest thing.
When I was living in London (admittedly almost 10 years ago), the only thing I found you could rely on as far as the beer selection was this:
Cheap lagers, pick two:
"Premiuim" lagers, pick one:
Stout, pick one:
Then 4-6 others, usually including a bitter, an ESB, a cider, and a few others (Newcastle, Caffrey's, Tennant's, Bass, etc.)
Of the three cheap lagers, I would say Carlsberg lagged well behind Carling and Heineken (though you could usually get it in bottles), and likewise Stella was a more popular "premium" lager by about 2:1 over Kronenberg. Then again, this was ten years ago so the landscape easily could've shifted drastically. However, saying a pub isn't British enough because they don't carry relatively crappy lagers from Denmark and France is probably pushing it. I would say it's much more significant that the HB has 5 cask pumps, which is far more than I've seen anywhere outside the UK.
All that said, there's no way an British pub in this town could ever stay in business actually duplicating the experience of a real British pub. Frankly, we are very much used to drinking much better beer and eating much better food than you find in most British pubs. At the pub I worked in over there, the top sellers were Budweiser, Heineken, and Carling, two of which are absolute piss and the third is only a marginal improvement. And food options consisted of crisps and Twiglets. That would never fly in this town.