The Bullingdon Club still exists, but essentially in name only. There are four members left at the moment, and their names aren't that much of a secret if you can be bothered to ask around. Rahs in tailcoats running around the town are usually OUCA members thinking they'd like to be in the BC, but aren't.
Other clubs like the Assassins and Piers Gaveston are more popular, but mostly cater to your typical coked up rah. The main secret society event is PGs' big termly party, held at a secret location in the middle of nowhere and attended by a few prominent socialites, which usually descends into a sex and drugs orgy. It's not hard to go along and see it if you have a car and know someone on the committee.