Ms Cooper addressed Mr Cameron during today’s Prime Minister’s Questions in the House of Commons.
She claimed he had put Britain’s reputation “to shame” by refusing to take in unaccompanied child refugees who are stranded in Europe after fleeing conflict in Syria.
And she called on him to change his mind.
Ms Cooper delivered her impassioned speech after the government defeated a House of Lords bid for the UK to take in 3,000 unaccompanied refugees who had reached Europe by a majority of 18 votes, on Monday.
And 294 MPs voted to block an amendment tabled by Lord Alf Dubs to the Immigration Bill that would have forced the government into providing new homes for the youngsters.
The House of Lords yesterday voted in support of a new proposal, this time calling on ministers to relocate a ‘specified number’ of the child refugees, to be decided by the government.
In the House of Commons today Mr Cameron said that children were “safe” once they entered the EU.
Ms Cooper, responding, said: “The Prime Minister has suggested that child refugees alone in Europe are safe.
“There are children’s homes full in Italy and Greece. Over a thousand children will sleep rough in Greece alone tonight.
“How are they safe? Ten thousand children have disappeared in Europe, how are they safe?
“The agencies say children are committing ‘survival sex’ – they are being abused, subject to prostitution and rape.
“It is not insulting other European countries to offer to help. They want us to help.
“So will he reconsider his position on Alf Dubs amendment before it comes back to vote, and stop with his attitude to loan child refugees, putting this house and this country to shame.”
She received a round of applause from the opposition benches.
Mr Cameron said the best way to help child refugees was “by taking them from refugee camps, taking them from Lebanon, taking them from Jordan, taking them when they come to this country”.
He said: “That’s what we’re doing and we have a proud record and nothing to be ashamed of.”
The government has said it wants to protect vulnerable refugees but has raised concerns that offering a safe place to lone children already in Europe may mean the minors could be exploited by trafficking gangs.