Local councils have accused the Home Office of ignoring offers to house hundreds of unaccompanied child migrants, as controversy grows over the announcement that only 150 more children would be accepted under the so-called Dubs amendment.

Announcing the cap last month, Home Office officials claimed that it was necessary because no more spaces were available to accommodate them. However, freedom of information responses collated by the Observer from dozens of UK councils paint a very different picture. There are at least 368 more spaces available for unaccompanied minors in the UK, under the national transfer scheme for asylum-seeking children.

These include 73 spaces in Birmingham and 41 in the north-west England region of councils. The overall total could be much higher as a significant number of councils have not yet responded to the freedom of information request. Several local authorities confirmed they have capacity for more child refugees and have communicated to the Home Office their wish to take more children under the Dubs amendment, aimed at housing unaccompanied minors from across Europe. The offers, they say, have been ignored.

Lewisham Council in south-east London offered to take 23 Dubs children. One has arrived so far. Bristol offered to accept 10 Dubs children, but has not received any. Glasgow offered to accept 35 children, but received 19. In home secretary Amber Rudd’s constituency of Hastings and Rye, there are 48 spaces available for unaccompanied minors.

On Thursday, Rudd, explaining her stance on child refugees, stated: “The Dubs amendment required us to consult local authorities on how many additional children they can manage and that is exactly what we did.” Critics argue that the Home Office made inadequate efforts to examine the capacity in the system for child refugees, some claiming the issue is causing tensions between government and local authorities.

Council documents seen by the Observer accuse Home Office officials of falsely claiming that some local authorities had reneged on offers to accept extra child refugees. One letter, from a senior council official to the Home Office, demands an apology for spreading “inaccurate comments”, given that the Home Office had refused to accept the council’s offer of taking extra child refugees.

Separately, Stephen Cowan, council leader for Hammersmith and Fulham in west London, revealed that his staff reported that the Home Office threatened “retribution” if they went public to criticise the Home Office on the issue of “Dubs children”. Cowan told the Observer: “One of our officials came in and said he’s been given a very clear indication there would be payback, retribution. The Home Office have gone out of their way to thwart every single attempt to act not just on the spirit of the Dubs amendment but on its specific terms.”

Bishop Jonathan Clark, who has been working closely with Citizens UK’s Safe Passage project, urged the Home Office to reappraise the UK’s capacity for accepting more child refugees. Clark said: “We appeal to the government to reconsult with local authorities to gain a realistic picture of their capacity to take child refugees. Many have told us that they are ready and willing to take more. The outpouring of public outrage at the potential closure of the Dubs scheme shows that Britain is ready and willing to help some of the most vulnerable child refugees in Europe. Government needs to listen.”

Alf Dubs, the peer who led the fight to secure sanctuary in the UK for refugee children, recently urged Rudd to put a call out to all local authorities asking which still have capacity to take refugee children from Europe. Most of the 150 child refugees still scheduled to enter Britain under the Dubs amendment are expected to be taken from Greece. However, sources close to the Dubs process have revealed that there is only one Home Office official in the country and charities there say there is no evidence that anything is happening.

On Thursday, MPs voted 254-1 in favour of keeping open the Dubs scheme and called on the government to continue consulting local authorities over their capacity to take more child refugees. The result, in which 20 Conservatives backed a continuation of the Dubs scheme, comes ahead of a full parliamentary vote on Tuesday to try to force the government to keep the option open.

A Home Office spokesperson said: “The government has significantly increased the funding it provides to local authorities who look after unaccompanied asylum-seeking children. It’s vital that we get the balance right between enabling eligible children to come to the UK as quickly as possible and ensuring local authorities have capacity to host them and provide them with the support they will need. We are committed to supporting vulnerable children who are caught up in conflict and danger and in the last year alone we have provided refuge or other forms of leave to more than 8,000 children.”