The government has been accused of acting in a “morally reprehensible” way after the Home Office confirmed it was planning to strip families of the automatic right to benefits if their asylum applications were rejected.

The Refugee Council expressed “grave concerns” as the Home Office minister James Brokenshire defended plans to remove automatic benefits from families who do not win asylum as a way of signalling that the UK is not “a land of milk and honey”.

The row broke out after the Sunday Times reported that the government was planning to bring the rules for asylum seekers with children into line with the rules for those without children. This means that unsuccessful asylum seeker families would lose their automatic right to benefits which entitle parents and children to £36.95 a week each through the Azure card system.

Brokenshire said it was right to remove the automatic right to benefits from people who were in the UK on an illegal basis. He told BBC Radio 4’s The World This Weekend: “We already have a system where, at the moment, if you don’t have a legitimate humanitarian claim you would lose your entitlement to support.

“What we are looking at now is family groups which continue to maintain that automatically against a backdrop of people trying to present the UK as somehow the land of milk and honey and that somehow if you get here you automatically are entitled to welfare.

“We think it is right that if you don’t have that claim – in essence you are here illegally – there should not be an automatic right to receive that benefit. That is why we are consulting to check on how we can still provide assistance to those in need who cannot leave the UK but equally there isn’t some automatic obtaining of welfare if you don’t have the right to be here.”

Lisa Doyle, the Refugee Council’s head of advocacy, condemned the government plan. Doyle said: “We have grave concerns about the government’s proposals to remove support from some of the most vulnerable families in the UK, many of whom fear there is real risk of serious harm or persecution to them and their children if returned to their countries of origin.

“We know that the government frequently gets life-and-death decisions on asylum claims wrong, as nearly 30% of appeals are successful. This harsh proposal seems to be based on the flawed logic that making families destitute will coerce them into going home.

“The government has a duty to protect all children in this country and previous governments have recognised it is morally reprehensible to take support away from families with children.”

The move by the government came as Theresa May, the home secretary, joined forces with her French counterpart, Bernard Cazeneuve, to send a signal to would-be migrants that they will not necessarily face a warm welcome. “Our streets are not paved with gold,” they wrote in a joint article for the Sunday Telegraph.

More than 200 migrants attempt to breach the inner fences of the Eurotunnel in Coquelles, near Calais, on Saturday night. Guardian

The two ministers warned that the world was facing a global migration crisis as they pledged to offer refuge to those fleeing conflict or persecution. But they said it was important to break the link between “crossing the Mediterranean and achieving settlement in Europe”.

May and Cazeneuve wrote: “Ultimately, the long-term answer to this problem lies in reducing the number of migrants who are crossing into Europe from Africa. Many see Europe, and particularly Britain, as somewhere that offers the prospect of financial gain. This is not the case – our streets are not paved with gold.”

Rev Trevor Willmott, the bishop of Dover, accused David Cameron of using “unhelpful” language after the prime minister described migrants trying to reach Britain as a “swarm” and promised to introduce strong-arm tactics, including extra sniffer dogs and fencing, at Calais.

On Saturday Downing Street announced it had also agreed with France to bolster security around Eurotunnel, with reinforcements joining the 200 guards already on patrol. Extra CCTV, infrared detectors and floodlighting will also be funded.

The bishop told the Observer: “We’ve become an increasingly harsh world, and when we become harsh with each other and forget our humanity then we end up in these standoff positions. We need to rediscover what it is to be a human, and that every human being matters.”