The government had previously said it would allow up to 3,000 children into the UK when the Dubs amendment was passed last year.
At the time, Downing Street defended the cap by saying there was a "limit to the capacity" councils could provide.
But it later emerged some areas had offered to house more child refugees and they had not been factored into the 350 figure.
In a written statement to Parliament, Robert Goodwill, Home Office minister, said: "The Home Office... believed that two regions in England had not provided responses after the consultation closed.
"The Home Office recently discovered that one of the regions had sent a return.
"We are now including their pledges in the specified number for the purposes of section 67 of the Immigration Act 2016."