The London Cocktail Club, perhaps you've been? They have "locations" at Covent Garden (6-7 Great Newport Street) Goodge Street (no 61) and New Oxford Street (224 Shaftsbury Ave).
I have been to two of these and both were great, as well as distinctly different.
The first at New Oxford Street (and run by my friend Sarah) was buzzing even by 6.30pm. They also have a fabulous cocktail hour but with the caveat of having to have the same cocktail on the 2-4-1 we chose to go "a la carte" and I started with the Bacon Martini aka heaven in a glass. There were others but this was the most memorable. And did I mention the mugs of (free) tasty pop corn to accompany your drink?!
The design of the bar means that there is privacy to be had, with pillars to peer round and various bunkers to be booked, even finding the toilets is a challenge for the evening. The staff are friendly and more than happy to accomodate the roudy birthday groups with a smile.
Somewhat like the Covent Garden Cocktail Club that is downstairs and members only though this is bookable and free to join. Don't let the huge mirrors on the walls decieve you, this place is not big so hold onto your cocktail if standing near the bar. I am not sure that the skills behind the bar are the same standard as at New Oxford Street but the barmen are friendly, clearly enjoying themselves and fully behind the mid 90's disco soundtrack they were rocking on a Saturday night - total crowd pleaser.