I had great (!) Martinis at Browns hotel, the Donovan bar. May be a tad small for us though.There are a number of options.
I doubt someone will offer his club for an eclectic gathering of strangers, but Duke's Hotel - although on the tourist trail - serves the best martini in London (off St. James's Street). The Lanesborough Hotel on Hyde Park Corner is not bad, and has better capacity for a larger gathering.
I'm gonna try to make it as well, so count me in.