The Advertising Standards Authority (ASA) said it began the investigation after receiving 60 complaints expressing concerns that the adverts were “reminiscent of slogans used by racist groups to attack immigrants in the past”.
In addition, the regulator said some complainants have challenged whether a claim reading “106 arrests last week in your area” was misleading.
The ASA’s probe is in addition to another investigation by the Equality and Human Rights Commission (EHRC) into immigration checks across the country.
The EHRC launched the probe after it was claimed that the spot checks – conducted at transport hubs up and down the country – were being carried out by border officials purely on the basis of ethnicity.
An ASA spokesman said: “Complainants have expressed concerns that the ad, in particular the phrase ‘Go Home’, is offensive and irresponsible because it is reminiscent of slogans used by racist groups to attack immigrants in the past and could incite or exacerbate racial hatred and tensions in multicultural communities.
“Separately, some complainants have challenged whether the claim ‘106 arrests last week in your area’ is misleading.
“They’ve also challenged whether it is misleading because it implies arrest is the automatic consequence of remaining in the UK without permission. We will publish our findings in due course.”
Last month, adverts displayed on billboards on vans in six London boroughs told overstaying migrants: “Go home, or you’ll be picked up and deported.”
The campaign may be extended nationwide.
Migrant groups, Labour politicians and unions reacted with anger and disgust.
Chris Bryant MP, Labour’s shadow immigration minister, said: “This is another embarrassing blow to a government which continues to fail to deal with immigration. With more people absconding at the border and fewer illegal immigrants being returned, David Cameron and Theresa May can’t even get the basics right, stumbling from one shambles to another.
“You’ve got to question the government’s competence. We need effective action on immigration, not offensive stunts.”
A spokesman for the Home Office said: “We can confirm we are in contact with the ASA over this investigation and we will respond in due course.”
Liberal Democrat Business Secretary Vince Cable has previously described the scheme as “stupid and offensive” and Muhammed Butt, leader of Brent Council in London, said it was “an act of desperation”.
Lord Ouseley, former chief executive of the Commission for Racial Equality, also criticised the van campaign.
The crossbench peer said it was possible to remove illegal immigrants without being “nasty”. He said: “What we have got is an advertisement which is actually contributing to a climate in which there is an element of racism and xenophobia.”
He added: “I think this is absolutely below the belt and it’s aimed at reinforcing the nastiness of the Conservative Party, which it should seek to avoid.”
But backbench Tory MP Peter Bone said if the pilot is effective it should be rolled out across the country.
He said: “If this works and people voluntarily go home who have been afraid to go before because they have been worried about getting arrested and if it does anything to tackle the evil criminal gangs that bring people here unlawfully then it’s a good thing.”