An evaluation report of the Government's 'Go Home' van pilot has revealed the phone number used in the near £10,000 campaign, dubbed Operation Vaken, received a total of 1,561 text messages - but 1,034 were hoaxes.
Around 17 hours of Home Office staff time were required to deal with the hoax messages, the report added.
Last week, Home Secretary Theresa May admitted the vans were "too much of a blunt instrument" and will not be rolled out nationwide.
The Government has admitted that of 60 people who voluntarily left the country during its controversial 'Go Home' van pilot, just over one sixth "had seen the ad vans themselves".
Shadow Home Secretary Yvette Cooper has branded the pilot, which has since been abandoned, a "complete gimmick".
She added: "It is no surprise that only two percent of those contacting the Ad Van number were those wanting to leave the country.
"And despite all the publicity the Ad Vans got, and the claims made by Downing Street, the evaluation shows that less than a dozen people who left were linked to the vans. And even these figures may not be reliable."
Downing Street defended the way the scheme had been handled and denied that the Government had shown "poor judgment" over the van campaign.
"I wouldn't accept that at all," the Prime Minister's official spokesman said.
At a regular briefing in Westminster he said: "The right thing to do is to look at a range of ways of tackling illegal immigration. This was one of them. It was piloted and then a decision not to proceed resulted on the basis of the analysis of the pilot."