Reform UK has hit back at both the Archbishop of York and the government following criticism of its immigration policies.

Leader Nigel Farage announced the party’s flagship immigration plan during a flashy news conference held at an aircraft hangar in Oxford on Tuesday.

The party pledged to deport anybody who comes to the UK illegally, regardless of whether they might come to harm, and said it would pay countries with questionable human rights records – such as Afghanistan – to take people back.

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It also said it would leave numerous international agreements, and revoke the Human Rights Act, in order to do this.

The policy was criticised by the Conservatives, who said Mr Farage was “copying our homework”, while parties such as the Liberal Democrats and the Greens condemned it.

But the plan came under fire from an altogether different angle on Saturday, when the Archbishop of York accused it of being an “isolationist, short-term kneejerk” approach, with no “long-term solutions”.

Stephen Cottrell, who is the acting head of the Church of England, told Sunday Morning With Trevor Phillips that he had “every sympathy” with those who find the issue of immigration tricky. But he said Reform UK’s plan does “nothing to address the issue of what brings people to this country”, and would in fact, make “the problem worse”.

Speaking on the same programme, Richard Tice, Reform’s deputy leader, responded to the archbishop’s criticisms, saying that “all of it is wrong”.

The MP for Boston and Skegness said he was a Christian who “enjoys” the church – but that the “role of the archbishop is not actually to interfere with international migration policies”.

Mr Tice then turned his fire on the government, accusing ministers of being “more interested in protecting the rights of people who’ve come here illegally… than looking after the rights of British citizens”.

He accused ministers of having “abandoned” their duty of “looking after the interests of British citizens”.

Mr Tice reaffirmed his party’s policy that the UK should leave the European Convention on Human Rights (ECHR), calling it a “70-year-old, out-of-date, unfit-for-purpose agreement”.

The Reform UK deputy leader also:

• Defended plans to pay the Taliban to take migrants back, comparing it to doing business deals with “people you don’t like”

• Said the Royal Navy should be deployed in the English Channel as a “deterrent”, but added: “We’re not saying sink the boats”

• Urged the government to call an early general election

Meanwhile, Bridget Phillipson, the education secretary, told Sky News that Reform “want to provoke anger, but they don’t actually want to solve the problems that we face in front of us”.

She told Sunday Morning With Trevor Phillips the UK had a “proud tradition [of] supporting those facing persecution”.

But she added: “We will make sure that people who have no right to be in this country are removed from this country. That’s right. It’s what people expect. It’s what this government will deliver.”

Ms Phillipson also insisted there “needs to be reform of the ECHR” and said the home secretary is “looking at the article eight provisions”, which cover the right to a private and family life, to see “whether they need updating and reforming for the modern age”.

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However, she refused to say what the government would do if it is found that the ECHR is unreformable. Instead, she defended Labour’s position of staying in the governance of the convention, saying that honouring the “rule of law” is important.

She added: “Our standing in the world matters if we want to strike trade deals with countries. We need to be a country that’s taken seriously. We need to be a country that honours our obligations and honours the rule of law.”

Ms Phillipson was also drawn on the recent court ruling in favour of the Home Office, which overturned an injunction banning The Bell Hotel in Epping from housing asylum seekers.

Challenged on whether the government is prioritising the rights of asylum seekers over British citizens, she said it “is about a balance of rights”.

The cabinet minister also repeated the government’s plans to end the use of hotels to house asylum seekers by 2029.

Shadow Cabinet Office minister Alex Burghart said the Conservatives would be willing to leave the ECHR – if this route is recommended to them.

The Tories have asked a senior judge to look into the “legal intricacies” of leaving the convention, which he said is “not straightforward”. He said when the party receives that report, it will then make a decision.

Challenged on whether the Tories will leave if that is what the report recommends, he added: “If that’s what’s necessary, we will do it.”

Mr Burghart also said he believed the previous Conservative government’s biggest mistake was that “we did not go far enough on overruling human rights legislation”, which prevented it from “taking the tough action that was absolutely necessary”.

But he added the Conservatives have now “put forward very clear legislation that would solve this problem” – though he concluded Labour “isn’t going to do it” so the problem “is going to get worse”.