They also rejected an earlier apology issued by a spokesman for the bar.
The icecream-based cocktails are topped with miniature plastic toy soldiers.
A spokesman had claimed that perception in London was “very different” to Northern Ireland while at the same time saying the organisation was “highly apologetic” to those offended.
But the apology was dismissed by those whose lives were devastated by Bloody Sunday.
Kate Nash, whose teenage brother William was one of 14 men and boys shot dead in Derry’s Bogside on January 30, 1972, said yesterday: “Perception is no different there than here, people everywhere are the same.
“Everybody knows what happened on Bloody Sunday was terribly wrong and even the Prime Minister said so.
“It is shocking at how cruel some people can be — who would think up something like this?
“You can understand somebody maybe naming a cocktail without knowing what they were doing, but to put soldier on top — that is obviously a dig at what happened.
“That took a fair amount of thought and it was intended.
“They better not try to apologise to me personally, because I wouldn’t accept it. It’s disgraceful.”
Ms Nash added that she now intended talking to her lawyer over the matter.
“To try and make a joke of Bloody Sunday is laughing at slaughter, at murder,” she said.
John Kelly, whose brother Michael was also one of the teenagers killed on Bloody Sunday, said the families were outraged.
“They should be ashamed of themselves and they should withdraw this immediately from their menu,” he said.
SDLP Foyle MLA Colum Eastwood has written to the bar requesting the drink's removal.
He said: “I think any right-thinking person will be shocked and annoyed that such a drink is being sold in London.”
There was no one available from the Adventure Bar yesterday to respond to the criticism.