Britain would face a mass influx of refugees from Calais if the country voted to pull out of the European Union, a former Conservative immigration minister has warned.

In an attack on Eurosceptics in his own party, Damian Green said it was “simplistic” and “flawed” to suggest that withdrawing from the EU would give Britain greater control over its borders.

Instead, he suggested, leaving Europe would lead to a huge increase in refugees entering Britain as France would no longer be under any obligation to prevent migrants from crossing the Channel.

“The fact that there are currently thousands trying to get to Britain, causing difficulties in and around Calais, shows that the French are prepared to put up with the difficult practical consequences of meeting their obligations to the UK,” Mr Green wrote in a pamphlet for the group Conservative European Mainstream. He went on: “Does anyone seriously imagine that they would continue to do this if we left the EU?”

And he added: “Things are already difficult enough in Kent with the problems at Calais. It would be perverse to make these even worse thanks to a deliberate act of national policy, alienating our nearest neighbour and thereby tearing up an agreement which works much more to our advantage than theirs.

“The emotional appeal of ‘taking control of our own borders’, which anti-Europeans see as one of their strongest arguments, is a deeply flawed concept.”

Mr Green’s comments coincided with an attack by another former Tory minister on the Home Secretary, Theresa May, for her tough line on immigration.

David Willetts, who was the minister for universities, said Ms May’s suggestion that 96,000 more students were arriving each year than were leaving was based on “unreliable” statistics and should be ignored. “People who come here to study should study, perhaps do some post-study work and then go back to their country,” he told BBC Radio 4’s Today programme.

“My disagreement is that the figure that was being cited for the number of students staying on is very unreliable. It is a widely disputed and doubted figure and would not be a solid basis for policy.”

Mr Willetts said the information came from the International Passenger Survey (IPS), but had been questioned by bodies including the Commons Public Accounts Committee. “I don’t think it is a reasonable indicator. It is based on a survey – by the time you get down to the number of students – of a few hundred students,” he said.

The former Tory MP said that in some cases people were recorded as students when they arrived but classed as workers when they left.

Other “better and more reliable” research by the Home Office between 2007 and 2012 indicated just 2 per cent of students failed to comply with their visa requirements.