Withdrawal from the EU could undermine Britain's co-operation with European partners in the fight against terrorism and international crime, David Cameron has suggested.
The suggestion came after Downing Street sparked fury among Eurosceptics by claiming Brexit could free thousands of migrants in the Calais "Jungle" to travel to the UK and potentially create tent cities in towns like Folkestone.
Advocates of withdrawal accused Number 10 of "scaremongering" over its claim that France could tear up the 2003 Le Touquet agreement which requires checks on cross-Channel lorries and trains to be carried on French soil.
But Mr Cameron raised the prospect that British withdrawal would put in doubt not only this arrangement, but also cross-border co-operation over terrorism and organised crime.
"If we can get this deal in Europe, if we can this renegotiation fixed and we can stay in a reformed Europe, you know what you get," said the PM.
"You know that the borders stay in Calais. You know that we have a seat determining the rules when it comes to the future of Europe.
"You know that we have that vital information, whether it's about terrorists or criminals travelling around Europe, because we are part of those organisations."
He added: "The people who want to take a different path have to start answering some questions about what it would look like if we are not in that organisation and not party to those rules. I know they fear that, but the time will come pretty soon where they have to start answering some of those questions."
Asked whether Mr Cameron was concerned that information-sharing about terrorists could be scaled back if Britain left the EU, a Downing Street spokesman said: "The point the PM was making is that as part of the EU, we have a very strong and positive working relationship with other EU nations and that works on a number of different levels in a number of different areas.
"Obviously, security is a core one. He talked specifically about the issue in Calais, but it is reflective of the fact that being part of the EU means there is that relationship with other member states."
Earlier, a Number 10 spokesman said it was a "perfectly feasible scenario" that quitting the EU could result in Paris ending co-operation over border checks and "thousands of asylum seekers pitching up in south-east England effectively overnight".
He said he could not rule out the suggestion the influx would be so great and sudden that it would result in Jungle-style camps being created in port towns such as Folkestone.
Eurosceptic former defence secretary Liam Fox said he was "sad and disappointed to see our Prime Minister stoop to this level of scaremongering", while fellow Conservative MP Sarah Wollaston said Mr Cameron was "taking voters for fools".
Ukip's migration spokesman Steven Woolfe said the warning was "based on fear, negativity and a falsehood" that the deal was connected to Brussels rather than a bi-lateral agreement between Britain and France.
Senior Tory David Davis added: "We already have a process where air carriers transporting passengers with no visa are fined as well as being responsible for returning people they have flown to the country illegally. There is no reason why the same policy would not work for trains and ferries. And we should spend a small fraction of the savings from our current EU budget contributions on enhancing our border controls and ensuring that they operate effectively."
But Mr Cameron insisted: "There are any number of opposition politicians in France who would love to tear up the excellent agreement we have with France to make sure that we have our borders on their side of the Channel.
"I don't think we should give those politicians any excuse to do that."
Downing Street's position was backed by Rob Whiteman, a former chief executive of the UK Border Agency, who said there was "not much upside for the French" in the current arrangement.
"If you're found in a concealed vehicle, you're a clandestine, once you set foot on British soil you can claim asylum whereas if you're found in a vehicle on French soil you can't claim asylum in Britain, Mr Whiteman told BBC Radio 4's Today programme.
"Before that treaty was put in place asylum claims were running at 80,000 a year in the UK. They are now running at about 30,000 a year so we would probably see, let's say, another 50,000 asylum claims a year which we used to get before the treaty came in."