Bishop Peter Hill of Barking has been speaking after ministers put together eligibility criteria for those coming into the UK.
It states that unaccompanied children must be 12 or under and at high risk of sexual exploitation, be 15 or under and either of Syrian or Sudanese nationality or be under 18 and a sibling of someone fitting this criteria.
Bishop Peter, who speaks on behalf of campaign group Citizens UK, said: "We are concerned that the Government's decision to only take children from Syria and Sudan from Calais is a mistaken application of their intent to ensure that only children from refugee producing countries are admitted to the UK.
"It is clear that Eritrean minors, for example, should be assessed as hailing from a 'refugee producing country'.
"Citizens UK's Safe Passage team estimates that 40 per cent of children in the Calais camp at the time of the demolition were Eritrean or Afghan. If the Home Office applies this criteria to the children who are being considered for sanctuary in the UK, it will be impossible to meet the Home Secretary's commitment to take 'half' of the children from Calais."
Responding to the criticism, Home Office Minister Robert Goodwill said: "We remain absolutely committed to bringing all eligible children to the UK as soon as possible.
"More than 300 children have been transferred from France since October 10, including resuming transfers over the weekend when another 19 girls assessed as being at high risk of sexual exploitation were brought to Scotland.
"The Government is getting on with the job of bringing eligible children over to the UK, working closely with the French authorities to ensure that both governments are working in the best interest of these children."
Mr Goodwill said Home Office staff are visiting centres in France to assess which children should be brought over to the UK and that "every opportunity" has been taken to speed up the process.
He also said the Home Office had restricted one of the eligibility criteria to just Syrian and Sudanese children because they are more likely to qualify for asylum.