How is the Hayes Society significant to Remains of the Day?

Stevens returns to the definition of a 'great' butler as determined by the Hayes Society - namely the butler must be a member of a 'distinguished' household. Stevens says his generation has a much more idealistic view of this definition of the word 'distinguished.' His generation believes that a distinguished man furthers the progress of humanity and aspires to noble causes. In his generation, other butlers are willing to leave not just over wages, but also over the moral worth of one's employers.

Butlers of Stevens' father's generation tended to see the world in terms of a ladder - and thus a distinguished household often represented the houses of royalty or the houses of lords. Any butler in his father's generation, then, simply climbed the ladder as high as possible - and the higher he went, the more professional prestige he accumulated. The Hayes Society endorsed this view as well. But later, the new generation viewed the world not as a ladder, but more as a 'wheel' - meaning that they cared about who they served, and they wanted to serve those to whom civilization was entrusted.

Firstly we are told that there was at one time a society of Butlers in England called "The Hayes Society".

That was something I had not previously considered - is there still such a society?

My Internet searching suggests that whereas some references in the Remains of The Day are factual ,the title of the organisation "The Hayes Society" is fictitious.