Controversial government adverts urging illegal immigrants to "go home" have been reported to the Advertising Standards Authority (ASA) by a Labour peer.

Lord Lipsey, a former member of the ASA's council, objected to a claim in the ads that there had been "106 arrests last week in your area", which he said was "grossly misleading".

The ads, displayed on billboards carried by vans in six London boroughs, tell overstaying migrants: "Go home or face arrest." The Home Office said that if the pilot proved successful, it could be extended across the country.

But the scheme was criticised on Tuesday by the deputy prime minister, Nick Clegg, who said it was not a "clever" way to deal with the issue and insisted no Liberal Democrat ministers were consulted before it went ahead.

Lipsey, who chairs the parliamentary all-party group on statistics, said he was concerned about whether the adverts' claim about numbers of arrests could be sustained.

The large-print claim of "106 arrests last week in your area" was followed by an asterisk referring viewers to a footnote in print too small to be read when the trailer was moving, indicating the week and boroughs involved.

But the Labour peer said that anyone who managed to read the footnote would find that the "huge" area referred to stretched from one side of London to the other, from Hounslow in the west to Dagenham in the east – and crucially included Heathrow airport.

It was likely that many of the detentions were of newly arrived would-be immigrants at the airport, said Lipsey, who told the ASA: "I believe the figures may well have been distorted by this inclusion, which would make the figures quoted misleading in breach of the codes."

Lipsey said the small print made clear the claim that the arrests took place "last week" was misleading, as the figures related to a period more than a fortnight before the ads were displayed.

And he added: "I do not believe that any inhabitant of Barking and Dagenham would believe their area to include Hounslow. Again, the government is deliberately misleading the public by aggregating figures over an area which no one would describe as theirs.

"If the government is to mount a campaign of this nature, it is incumbent on it to ensure that it does not exaggerate or lie, in breach of the advertising code of practice. On the face of things, this advert falls far short of the standards insisted on by the ASA. I have accordingly asked it to rule urgently on its acceptability."