Video report by ITV News Correspondent Rebecca Barry
Silkie Carlo, director of privacy campaign group Big Brother Watch, said: "It's extremely worrying to see that the Government doesn't have a basic grip on data protection, and that people receiving some of the highest honours have been put at risk because of this.
"It's a farcical and inexcusable mistake, especially given the new Data Protection Act passed by the Government last year - it clearly can't stick by its rules."
The Cabinet Office has apologised for the publication, which also included the addresses of serving police officers, other politicians and a host of sporting figures and celebrities.
A spokesman said: "A version of the New Year Honours 2020 list was published in error which contained recipients' addresses.
"The information was removed as soon as possible.
"We apologise to all those affected and are looking into how this happened.
"We have reported the matter to the ICO (Information Commissioner's Office) and are contacting all those affected directly."
Among them were the former director of public prosecutions Alison Saunders and ex-Conservative Party leader Mr Duncan Smith, the architect of the Universal Credit system, whose knighthood sparked a backlash from critics.
The Cabinet Office has said the information was available for about an hour, in the early hours of Saturday, December 28.
Hackney councillor and charity pioneer Mete Coban, who was handed an MBE for services to young people, said : "If those responsible have apologised and it is a genuine error, then there is not much more that can be done.
"I understand why others are concerned but most of my details are online because of the council work anyway.
"It is not ideal but what is done is done."
The ICO, which has the power to fine organisations for data breaches, said it was investigating.
A spokesman said: "In response to reports of a data breach involving the Cabinet Office and the NY Honours list, the ICO will be making enquiries."