Thanks for the links
Too bad, Archive.org didn't save this article, or save their "Showbiz Video" page for this day. From what I've read online, this wasn't really 'A Secret Gig', Amy just showed up while New Orleans jazz vocalist Corliss Randall was doing her residency there. The following is a post from the reviews section of allinlondon.co.uk made by an audience member that was there that night ...
Went to jazz after Dark on Wednesday night to celebrate my girlfriends birthday, we were a group of ten so we booked in advance to get a table in the music area. It is a lovely cool place with a great selection of tapas and an amusing cocktail list. They had a house band playing, a New Orleans jazz vocalist with pianist, bass and sax they were very entertaining. Suddenly to our amazement in walked Amy Winehouse with a group of friends – she is really lovely she chatted happily with everybody. They ordered jugs of cocktails and tapas just like us – to our joy the house band invited her up to sing. She sang two songs and she left the crowd overwhelmed.
Corliss Randall was also the Jazz After Dark residency artist when Amy did an impromptu there in Feb 2008