A bit of research suggests that the pub is Grade II listed and is around 125 years old. The St Stephen's Tavern only reopened in 2003, having been closed since the late 1980s for various reasons. It is perhaps for this reason that many Parliamentarians prefer to drink in the nearby Red Lion, and this is more of a Civil Servant pub.
Despite the lengthy closure, the pub has been refurbished to an excellent standard with the help of English Heritage. Your author also understands that it benefited from having many interior fittings kept in storage during the period of closure so it could be refitted to a near-original appearance.
For more information, see the Evening Standard's article here, from where much of the above is taken. The Standard would have us believe that former Prime Ministers Baldwin, Churchill and Macmillan drank here and there is no reason to doubt them.