The official campaign to leave the EU fronted by Michael Gove has been accused of “stoking the fires of prejudice” after it claimed that continued membership would put Britons in danger as a result of a high level of criminality among Turkish citizens.

In a potentially incendiary intervention – on the eve of an England v Turkey football match in Manchester – coordinated statements from a government minister and Vote Leave not only claimed that Turkey was about to join the EU, but that its citizens posed a threat to national security, as well as to public services.

An analysis by the Brexit campaign group cited higher levels of criminality and gun ownership in Turkey as evidence for their position, which was supported by a statement from Penny Mordaunt, a defence minister who backs Brexit.

Vote Leave said: “Since the birthrate in Turkey is so high, we can expect to see an additional million people added to the UK population from Turkey alone within eight years.

“This will not only increase the strain on Britain’s public services, but it will also create a number of threats to UK security. Crime is far higher in Turkey than the UK. Gun ownership is also more widespread. Because of the EU’s free movement laws, the government will not be able to exclude Turkish criminals from entering the UK.”

The controversial Vote Leave campaign poster. Photograph: Vote Leave

Despite Downing Street’s insistence that Turkey’s accession to the EU was not imminent, Mordaunt said in her statement that a vote to remain in the EU on 23 June was a vote in favour of Turks moving “here freely when they join the EU soon”.

A Vote Leave poster will be launched on Monday depicting an EU passport as an open door, with footprints leading through it. It will claim: “Turkey (population 76 million) is joining the EU. Vote Leave, take back control.”

These developments prompted criticism from a series of high-profile figures, including Trevor Phillips, a former chairman of the Equality and Human Rights Commission, who claimed it was a desperate ploy.

The Observer/Opinium’s latest on-line poll suggests 44% of UK adults will vote to remain in the EU, while 40% will vote to leave and 14% are undecided.

Trevor Phillips condemned the Vote Leave poster as a ‘desperate move’. Photograph: David Hartley/Rex/Shutterstock

Phillips said that, while the issue of immigration should be debated, the “latest assault from the Leave campaign seems to me to plumb the deepest depths”. He said: “There really isn’t any doubt that what they are appealing to here is straightforward prejudice. I can’t imagine what the sizeable, law-abiding, industrious Turkish community in the UK must feel when they hear this.

“This appears to be a straightforward admission that the Leave campaign has lost on every rational argument and now it is simply trying to stoke the fires of prejudice.”

Europe minister David Lidington said it was “complete fantasy” to suggest that Turkey or Albania would become members of the European Union within five years. “It is ridiculous,” he said.

The shadow justice secretary, Lord Falconer, said he was concerned by Vote Leave’s indifference to the damage to community relations caused by its claims. “It is dangerous and inflames racism to imply many of the Turks who are coming may be criminals with guns,” Falconer said. “I’m really concerned about the way the Brexiters appear utterly indifferent to the long-term damage they are doing.

“Argue their case by all means, but don’t descend into the gutter and poison good community relationships. Gove is showing no integrity whatsoever in what he says in the referendum debate.”

Vote Leave countered that the home secretary, Theresa May, had herself raised concerns about Turkish organised crime in April.

The London mayor, Sadiq Khan, will throw City Hall behind the Remain campaign on Monday, with a major social media drive, a series of set-piece speeches and newspaper advertising. From Sunday, the European Union flag will also be flown outside the mayor’s headquarters to symbolise its new position on the referendum.

On Friday, Gove, who is justice secretary, argued that Turkey and four other countries could join the EU as soon as 2020 and lead to 5.2 million extra people moving to the UK, a population the size of Scotland or four cities the size of Birmingham, putting intolerable pressure on the NHS.

In Vote Leave’s latest analysis it warns that Turkey will join the EU “in the next few years” and that its population is set to hit 82 million by 2020, many of whom will seek to come to Britain. It is claimed that, as well as threatening the UK’s security, the growing Turkish population in the UK will cost NHS maternity services an extra £400m within 10 years of the country joining the EU.

Mordaunt said: “We are currently sending over £1bn to Turkey to help it to join the EU. We must recognise the huge strain this will place on our NHS as more people come here, without giving it any chance of planning for such increased demand. Expansion is at the EU’s core. We have to be honest about the cost of EU membership for our public services today and in the future: and particularly what this will mean for the NHS unless we take back control and Vote Leave on 23 June.”

Professor Martin McKee, professor of European public health at the London School of Hygiene and Tropical Medicine, condemned Vote Leave’s claims about the future of the NHS. “It is unacceptable for Leave campaigners to keep dragging the NHS through the mud,” he said.