Where are you getting the idea that a lot of admirals are also members of the Federation Council? I haven't seen any recent'ish novels or anything in canon indicate that, but maybe I missed something?
He's referring to Star Trek IV: The Voyage Home.
During that film's scenes in the Federation Council Chambers, many of the council members are wearing uniform.
For my part, I like to assume that former serving officers are permitted to wear ceremonial uniform after leaving the service to enter politics, but that's just my fannish means of avoiding the problems TheGodBen