It is another van carrying a poster connected to immigration, touring ethnically diverse parts of London, but the message could hardly be more different from the government's version.

This poster van has been organised by the campaign group Liberty as a riposte to the Home Office's recent "Go Home" campaign.

The Home Office vans, which toured six London boroughs in a pilot scheme that ministers said could be extended nationwide, carried the wording: "In the UK illegally? Go home or face arrest."

Opponents, among them the business secretary, Vince Cable, labelled the scheme an offensive stunt. Some critics said the "go home" wording was reminiscent of racist slogans from the 1970s.

The Liberty van, which was spending Tuesday following part of the route of its Home Office equivalent, carries the message: "Stirring up tension and division in the UK illegally? Home Office, think again."

Rachel Robinson, a Liberty policy officer, who was spending the day in the van, said they had started their tour in Westminster. "We were outside the Home Office for a little while, and had some quizzical looks from officials. But it certainly seems to be having an impact."

The van then went north-west to Kensal Green and was about to go east to Walthamstow, she said. "We thought this was an excellent way to get the counter message out there. We want to offer an alternative message, which isn't about division and stirring up tension. That's what we're really trying to achieve."

Robinson said the civil liberties organisation was also handing out leaflets to people who had been caught up in a sweep against suspected illegal immigrants carried out last week by the UK Border Agency (UKBA), mainly at rail stations, in which officials appeared to target people on ethnic grounds.

The checks are being investigated by the Equality and Human Rights Commission and were condemned by the Ukip leader, Nigel Farage. Robinson said of the checks: "We think there are very good grounds for challenging the legality of these operations."