Reform UK has engaged in a war of words with the Church of England over the party’s plans to deport all asylum seekers who arrive in small boats, after the church’s most senior bishop called the proposal “isolationist, short-term [and] kneejerk”.

Richard Tice, the party’s deputy leader, hit back against the archbishop of York, Stephen Cottrell, on Sunday, accusing him of interfering in domestic politics.

This week Nigel Farage, Reform’s leader, announced the party’s migration policy, under which Britain would leave the European convention on human rights (ECHR) and deport people who arrive or have recently arrived by small boat from France.

Cottrell told Sky News’s Trevor Phillips: “We should actively resist the kind of isolationist, short-term, kneejerk – in this case, ‘send them home’. Mr Farage is saying the things he’s saying but he is not offering any long-term solution to the big issues which are convulsing our world, which lead to this.”

Responding on the same show, Tice rejected the criticism and urged the bishop, who is the acting head of the church while it searches for a new archbishop of Canterbury, to stay out of migration policy.

Asked which of Cottrell’s criticisms were wrong, Tice replied: “All of it’s wrong.”

He said: “I enjoy the church, I believe in God. But the role of the archbishop is not actually to interfere with international migration policies.”

Farage’s new asylum policy involves deporting asylum seekers who cross the Channel, even to countries such as Afghanistan and Eritrea. To do so, Reform is promising to take Britain out of the ECHR, the 1951 refugee convention, the UN convention against torture and the Council of Europe anti-trafficking convention.

A Reform government would then send teams of immigration officials into communities across the country to find people who have settled here after arriving as irregular migrants and deport them as well.

The party has struggled to answer detailed questions about how the policy would work and how much it would cost. Farage initially said women and children would be detained and deported as well as men, but a day later he appeared to row back on that, suggesting doing so was not “part of our plan”.

Asked by the Guardian why he had costed the proposals at £10bn when a thinktank had priced a similar plan by his former colleague Rupert Lowe at £47.5bn, Farage responded: “Zia [Yusuf, the senior Reform official] is very good at maths.”

Reform has also talked about deploying the navy to help it enforce its migration plans. Asked on Sunday whether its role would be simply to act as observers while small boats continued to cross, Tice replied: “Yes. In a sense, that’s what the Border Force are currently.”

Reform is looking to keep the pressure on the government to close asylum hotels even after a court ruled that ministers could continue to use the Bell hotel in Epping to house people whose claims had not yet been processed.

Bridget Phillipson, the education secretary, said on Sunday that the government would look to close hotels in an “orderly” way by the end of the parliament. “We can’t end up with hundreds of people just out on the street because a hotel has closed,” she said.

Separately, she appeared to put pressure on the prime minister and the chancellor to end the two-child benefit cap, which Cottrell warned was driving up child poverty.

“I’m ashamed of the very high numbers of children growing up in poverty that we see in our country,” she said, adding that bringing that level down was “what I came into politics to do”.

Asked specifically about the benefit cap, she said: “It’s not the only way we can lift children out of poverty, and of course, it does come with a big price tag. But we know that not acting also comes with serious consequences and impact too.”