I've sporadically encountered this right-wing, elite think tank in my journeys across the World Wide Web; and the material I encountered strongly suggested that they were among the top influentials in the ruling class. Having spent a lot of time in the Northwest of the US, I knew who Henry Jackson was (long time Senator from Washington state), and thus assumed that it was an American think tank--it's British. Actually, with this article written by a very astute author, it is now clear to me that the Society plays a key role in what historian Carroll Quigley has referred to as The Anglo-American Establishment (title of his very important book) which arose to dominant power after WWII and has become, what many refer to as, the US Empire, or simply the Empire (a 4th Reich?).
Also, the fact that this Society is British-based is a clear illustration of how the capitalist ruling class directorate of the Empire crossed national boundaries in the decades since WWII as described by Quigley. Subsequent to this development, they went on to thoroughly integrate the capitalists of many other countries into what is now familiar to most political analysts, a US-led Empire complete with its own army--NATO.
Senator Henry Jackson of Boeing's Washington state played a key role in bringing into the government important neoconservatives such as Paul Wolfowitz, Richard Perle, Elliot Abrams, Douglas Feith, Robert Kagan (and wife Victoria Nuland), Charles Horner, and James Woolsey .
...it is hugely important to understand [why] that HJS [Henry Jackson Society] and the interests it represents are so out of whack with not only what the vast majority of the public would agree with or desire, but even what most policymakers would want to see happening in the world.