The Government’s policy to send migrants to Rwanda would not stand up to the scrutiny of God, the head of the Church of England has said, as it was confirmed the Home Office’s most senior civil servant has concerns about the value for money of the scheme.

An exchange of letters published by the Home Office on Saturday night showed the department’s Permanent Secretary Matthew Rycroft warning Home Secretary Priti Patel that although it was “regular, proper and feasible for this policy to proceed”, there was “uncertainty surrounding the value for money of the proposal”.

But issuing a rare ministerial direction compelling the plans to go ahead despite the concern, Ms Patel said that “without action, costs will continue to rise, lives will continue to be lost”.

Earlier this week the Government announced plans to curb migrant crossings of the English Channel in small boats, and people who are deemed to have entered Britain by unlawful means since January 1 may be sent to Rwanda where they will be permitted to apply for asylum in the African country.

The measures have faced a fierce backlash from opposition parties, some within the Conservative Party, charities, and religious figures.

In his Easter sermon on Sunday, the Archbishop of Canterbury Justin Welby said “sub-contracting out our responsibilities, even to a country that seeks to do well, like Rwanda, is the opposite of the nature of God who himself took responsibility for our failures”.

The archbishop said there are “serious ethical questions about sending asylum seekers overseas”.

He said: “The details are for politics. The principle must stand the judgment of God, and it cannot. It cannot carry the weight of resurrection justice, of life conquering death. It cannot carry the weight of the resurrection that was first to the least valued, for it privileges the rich and strong.”

He was joined in his criticism by the Archbishop of York Stephen Cottrell, who used his Easter Sunday sermon at York Minster to say he found the policy “depressing and distressing”.

He said: “We can do better than this. We can do better than this because of what we see in Jesus Christ, the risen Christ, with a vision for our humanity where barriers are broken down, not new obstacles put in the path.

“After all, there is in law no such thing as an illegal asylum seeker. It is the people who exploit them that we need to crack down on, not our sisters and brothers in their need. We don’t need to build more barriers and cower in the darkness of the shadows they create.

“Do we want to continue to be known as a country that opens proper, legitimate pathways for all who flee violence, conflict and oppression, not just those from Ukraine, but also those fleeing other conflicts and the effect of climate change?”

A Home Office spokesperson said: “The UK has a proud history of supporting those in need of protection and our resettlement programmes have provided safe and legal routes to better futures for hundreds of thousands of people across the globe.

“However, the world is facing a global migration crisis on an unprecedented scale and change is needed to prevent vile people smugglers putting people’s lives at risk and to fix the broken global asylum system.

“Rwanda is a fundamentally safe and secure country with a track record of supporting asylum seekers. Under this agreement, they will process claims in accordance with the UN Refugee Convention, national and international human rights laws.”

The policy has enjoyed some support from Conservative MPs, who say the issue of small boats crossing the Channel is high on the priority list for constituents.

Ms Patel said she expected other countries to follow the UK’s example, suggesting Denmark could be among those to reproduce the Government’s “blueprint”, while the Home Office insisted its approach was not in breach of refugee agreements.

In his letter, Mr Rycroft warned the Home Secretary: “I do not believe sufficient evidence can be obtained to demonstrate that the policy will have a deterrent effect significant enough to make the policy value for money. This does not mean that the (measures) cannot have the appropriate deterrent effect; just that there is not sufficient evidence for me to conclude that it will.”

But Ms Patel said it would be “imprudent in my view, as Home Secretary, to allow the absence of quantifiable and dynamic modelling – which is inevitable when developing a response to global crises influenced by so many geopolitical factors such as climate change, war and conflict – to delay delivery of a policy that we believe will reduce illegal migration, save lives, and ultimately break the business model of the smuggling gangs”.