In an interview with Newsweek Europe, published on Thursday, the Ukip leader was asked which people should be allowed to migrate to the United Kingdom. He said: "People who do not have HIV, to be frank. That's a good start. And people with a skill," he said.
The chief executive of HIV/Aids charity Terrence Higgins Trust accused Farage of stooping to a "new level of ignorance" and Labour MP David Lammy said he was "trying to revive the very worst bigotry" of the 1980s.
Jones, who served for a year in Gordon Brown's government and introduced George Osborne at this year's Conservative Party conference, said Farage was "tapping into something important people are beginning to say throughout Britain".
"We should be saying, 'I don't want you to come into this country with a communicable disease'," he said. Jones said people would be thinking: "I don't really want you to come here and give me Aids."
Farage's comments are also a potential embarrassment to Douglas Carswell, who was elected as Ukip's first MP yesterday. Carswell's father was an Aids pioneer in the 1980s. Confronted by reporters in a media scrum [video above] on Friday morning, Carswell dodged questions on the issue.
Jones, who sits as a cross bench peer in the Lords, insisted it was not discriminatory to want to ban people who had HIV from coming to Britain. "I don't care if they are black, white, gay, straight, male, female, I couldn't give a monkeys," he said.
He added: "You're not here, so why should you come here? This isn't discriminatory against the person. You have a problem which could threaten our society and we actually don't want to weaken our society."
Jones made the remarks while taking part in the newspaper review on the BBC News channel late on Thursday evening. This morning The Guardian's front page led with Fargage's comments.
The peer's support for banning people with HIV was met with derision from fellow panellist, broadcaster Henry Bonsu. "Why would you equate somebody who is HIV positive with someone who has a murder conviction?" he asked.
Bonsu said Farage's comments were a "knee-jerk, nasty response. The kind of hysteria we saw in the 1980s and 1990s that saw all sorts of horrible headlines".
Hard to know where to start with this. Farage trying to revive the very worst bigotry of the 80s. Shameful. pic.twitter.com/qyWzdcPg26— David Lammy (@DavidLammy) October 9, 2014
The Terrence Higgins Trust's chief executive Dr Rosemary Gillespie said: "The idea that having HIV should be used as a black mark against someone's name is ridiculous, and shows an outrageous lack of understanding of the issue.
"It is to the UK's credit that for more than three decades successive governments, no matter their political stamp, have refused to put in place border controls against people living with HIV.
"Major international organisations, including the United Nations, agree that such draconian measures would have no impact on the epidemic. In bracketing those living with the condition with murderers, and suggesting there is no place for them in his vision of Britain, Mr Farage has stooped to a new level of ignorance."