The Archbishop of Canterbury has blasted the UK government over its failure to reunite unaccompanied refugee children in France with their families in Britain.

In the House of Lords on Tuesday, Archbishop Justin Welby contributed to a discussion on the government's plans to speed up the process for children in camps in Calais and Dunkirk.

"My Lords, the Question has been extremely specifically put about children who have families in this country; this is not about all unaccompanied children," the Archbishop said.

"My own diocese of Canterbury has taken on a staff member who is working in the Jungle, in co-ordination with a staff member taken on by the Catholic diocese of Arras. We are still having continual reports of delays for really quite young children who are not being brought across.

"Does the Minister not agree that where children – particularly young ones – have families in this country there is no reason why they should not be brought across within the day?"

The Minister of State at the Home Office, Baroness Williams of Trafford, responded: "My Lords, many of the children are coming here very quickly, but if any child has to stay over in the camp for any longer than it should that is one child too many.

"I commend the most reverend Primate on the work that Lambeth Palace is doing in taking its first family. We are clear that refugees in Calais should first of all claim asylum in France and then come over here through the Dublin process."

She said 120 children had come to the UK this year under the Dublin regulations, 70 of them from France.

Lord Alf Dubs, who himself fled Nazi Germany in 1939 and has been a prominent campaigner for child refugees, branded the situation "deplorable".

"My Lords, it cannot be in the best interests of any child to stay in Calais, in awful conditions with no proper safety or security apart from a few British NGOs. It is deplorable," he said.

"If the Minister would come to Calais – I was there last Saturday – she would see what I am talking about."

The debate comes as Unicef releases a new report today which accuses the UK government of putting children at risk of abuse and trafficking by not making it clear that children with family in the UK have a right to asylum.

"Today, nearly one in every 200 children in the world is a refugee. In the last few years we have seen huge numbers of children being forced to flee their homes, and take dangerous, desperate journeys, often on their own. Children on the move are at risk of the worst forms of abuse and harm and can easily fall victim to traffickers and other criminals" said Lily Caprani, Unicef UK deputy executive director.

"Many of these children wouldn't resort to such extreme measures if the UK Government made them aware that they may have a legal right to come to the UK safely and if they provided the resources to make that process happen before these terrible journeys begin." She added. "At the historic summits in New York this month, the UK has a chance to show vital leadership on this agenda."

The Report, Uprooted: The growing crisis for refugee and migrant children, reveals that 50 million children have been uprooted around the world, and 28 million of them driven from their homes. They make up about half of all refugees and more and more are crossing borders and making perilous journeys on their own.

Children make up 31 per cent of all refugees and migrants who have arrived by sea in 2016, Unicef said, and around 45 per cent of those stranded in south-east Europe.

Unicef urged the UK to take immediate action to offer more resettlement places to suffering children.