Only 11 people have left the country as a direct result of Theresa May's "go home or face arrest" van advertisements, the scheme's official evaluation report has revealed.

The Home Office's assessment confirms that the first person to leave the country as a result of the campaign was a Pakistani student who read about the vans in the Guardian. But it says that publicity came at a cost given the number of concerns expressed about the adverts.

The evaluation report also reveals that 1,561 text messages were received in response to the advert's invitation to text for free advice and help with travel documents. But unfortunately for the Home Office, 1,034 of the texts were hoax messages which took 17 hours of staff time to deal with.

The mobile billboard vans toured six London boroughs between 22 July and 22 August as part of a wider advertising campaign to encourage illegal immigrants to leave the UK. The vans drew widespread criticism, including claims that May was "borrowing the language of the 1970s National Front". Critics included the Ukip leader, Nigel Farage, and Liberal Democrat cabinet ministers.

The wider Home Office summer immigration enforcement campaign, Operation Vaken, included placing adverts in eight minority ethnic newspapers, postcards in shop windows, and leaflets and posters advertising immigration surgeries in buildings used by faith and charity groups.

The official evaluation report says that in total 60 people have left the UK voluntarily as a result of the campaign, with a further 65 cases currently in progress. Only 11 people left as a direct result of the van adverts and a further seven after seeing reports of the vans in the media or online. The report says the most effective medium, which led to almost half the overall number leaving the country, were the posters or leaflets advertising immigration surgeries.

The home secretary finally bowed to the wave of criticism last week and announced that the van pilot scheme would not be extended, saying it had been "too much of a blunt instrument".

The report reveals that there also no plans to repeat a separate pilot scheme, under which "ask about going home" posters were put up in two immigration reporting centres in Hounslow and Glasgow. These posters also drew sharp criticism from refugee welfare groups that they were offensive to asylum seekers who had fled for their lives and were required to attend the reporting centres. One poster showed a photograph of an aircraft and read: "This plane can take you home. We can book the tickets."

The immigration minister, Mark Harper, said this aspect of the campaign was being evaluated separately but there were no plans to repeat it.

Harper told MPs in a written ministerial statement that the Operation Vaken campaign had cost £9,740. He claimed that 60 voluntary removals connected to the pilot had "saved" £830,000 on the basis that an enforced removal cost £15,000 compared with £1,000 for a voluntary return. The Home Office calculation includes a figure of £4,250 a year for the estimated cost to public services of an illegal immigrant in Britain.

"The government will continue to enforce the immigration rules and promote voluntary departure schemes to those who have no right to be in the UK – backed up with arrest, detention and enforced removal where individuals refuse to comply with the immigration rules or present a danger to the UK public," said Harper.