Last week, Micheal Martin, the Irish deputy prime minister, said the UK's Rwanda policy was “impacting on Ireland” because people were “fearful” of staying in the UK and were seeking asylum in Ireland instead. The Irish claim 80 per cent of asylum seekers have crossed the border from Northern Ireland.

The Home Office has also admitted that it is unable to remove more than half of the 5,700 migrants it intends to deport to Rwanda in a document seen by The Times on Monday night.

Simon Harris, the Irish prime minister, has asked for proposals for a new law to be brought to his cabinet this week to pave the way for the return of migrants to the UK.

Sunak ‘determined to get our Rwanda scheme up and running'

However, asked on ITV News whether he would agree to a returns agreement with Ireland, Mr Sunak said: “We're not, I'm not interested in that. We're not going to accept returns from the EU via Ireland when the EU doesn't accept returns back to France where illegal migrants are coming from.

“Of course we're not going to do that. I'm determined to get our Rwanda scheme up and running because I want a deterrent.”

Asked if there was scope to negotiate a returns deal with the EU, Mr Sunak said: “No. I'm focused squarely on getting our Rwanda scheme up and running. I want the deterrent which will say that if you come to our country illegally, you will not be able to stay and you will be removed either to your own country if it's safe or Rwanda.

“That's why I've worked so hard at this. That's why we've done all the prep work for this. And actually I want that deterrent up and running and I'm confident that it will work.”

It came as Mr Martin met with Chris Heaton-Harris, the Secretary of State for Northern Ireland, at the British-Irish Intergovernmental Conference in London on Monday.

Mr Martin told British officials that legislation being prepared to enable Dublin to legally send back asylum seekers to the UK was to deal with a decision by the Irish High Court. That decision overturned the designation of the UK as a “safe country”. The new Irish law, to be presented on Tuesday, provides a replacement legal base for migrant returns.

UK ‘not in the business of having more Channel migrants'

However, Mr Heaton-Harris warned that any migrant returns deal would have to be EU-wide and not just with Ireland.

He added that the UK was prepared to work with Ireland to prevent abuse of the Common Travel Area between the two countries.

“If this legislation is, as I believe it is and I've been assured it is, just setting us back in time to where we were and what we were dealing with, then I'm comfortable with that,” Mr Heaton-Harris said.

“But we are fully behind implementing our Rwanda scheme.”

Mr Martin said: “The Common Travel Area, there will be ongoing discussions around that and it's been overall beneficial to Irish citizens and to UK citizens and we want to maintain those benefits. I think the optimal way to deal with issues around migration is to continue discussion in the context of the Common Travel framework.”

Mr Martin ruled out Ireland launching a legal challenge in the European Court of Human Rights against the Rwanda Plan. Dublin has sued the UK in the Strasbourg court over its Legacy Act, which is an effective amnesty for Troubles-era killers.

“We're not going to the European court on this one,” he said.

Mel Stride, Secretary of State for Work and Pensions, said on Monday morning: “We are not in the business of having more Channel migrants in the UK. We have a situation where people are coming across from France illegally. The French are not prepared to take back the illegal migrants. I don't see why we should have any different situation.

“There are going to be discussions between the Irish Government and ours. I very much doubt we are going to end up in a position where we are going to say we are going to be taking anybody back – not least because, when it comes to France and other EU countries, they are not in the business of taking people back either.”

Helen McEntee, the Irish Justice Minister, pulled out of the conference in what was seen as a tit-for-tat move following a decision on Sunday by James Cleverly, the Home Secretary, to cancel their meeting. Home Office sources cited a diary clash.

Immigration to Ireland rose by 32 per cent in the year ending last April, with asylum seekers accounting for more than 13,000 of over 140,000 arrivals.

Mr Harris said on Sunday: “Every country is entitled to have its own migration policy, but I certainly don't intend to allow anybody else's migration policy to affect the integrity of our own one. This country will not, in any way, shape or form, provide a loophole for anybody else's migration challenges. That's very clear.”

However, Mr Stride was unapologetic about the Rwanda policy. Asked whether it was designed to force migrants into Ireland, he denied that was the case, saying: “The design is to ensure there is a deterrent effect.

“We passed the Rwanda Bill that means those coming here illegally can expect to be removed to Rwanda. What we are already seeing is a deterrent effect kicking in. That's why we are seeing people moving from the UK into Ireland.”

No post-Brexit returns agreement

Before Brexit, the return of migrants to EU countries was governed by the Dublin Agreement, under which migrants could be sent back to a safe third country through which they had passed before arriving at their destination.

This meant asylum seekers arriving in Ireland from the UK, or migrants reaching the UK from France could be returned if it could be shown that they had passed through a safe third country – that is, the UK or France.

‌But the UK left the scheme when it departed the EU and no successor agreement was signed during the Brexit talks, meaning there are no formal returns agreements in place between EU countries and the UK.

A post-Brexit provision was, however, made in the case of the UK and Ireland, which meant Ireland could return asylum seekers to Britain. No asylum seeker has been returned to Ireland, or vice-versa, under this post-Brexit arrangement since it was struck.

But the Irish High Court last month ruled that the Irish government's declaration of the UK as a “safe third country” to which it could return asylum seekers was unlawful, as a result of the Rwanda Bill. The emergency legislation proposal seeks to overturn this judgment.

Rwanda plan makes returns agreement ‘unpalatable'

EU sources told The Telegraph that the Rwanda plan has made a migrants returns agreement with Britain unpalatable for too many “progressive” European Union governments.

While the bloc's conservative leaders see no merit in a UK-EU returns deal because it would result in “more” asylum seekers being sent from Britain to the Continent.

“The Rwanda stuff will make a deal unpalatable to a whole slew of progressive governments on the EU side,” an EU diplomat said.

“And then there's the question of what the EU gains from a deal with the EU? A deal might only lead to more returns from the UK to the EU. That's not going to win you any votes on the conservative, so what's the incentive?”

The EU will hold bloc-wide elections for the European Parliament in June amid fears populist and nationalist parties will win in at least nine countries on the back of anger over mass migration and Net Zero policies.

Sources said there was also little appetite in sitting down with Britain while the EU is engulfed in its own migration crisis.

“I don't see much interest in a UK-EU migration deal until we've properly sorted out our own migration mess first,” a Brussels insider said.

“Yes, we've agreed on the pact, but that doesn't enter into force for another two years,” they added, referring to new border measures to halt illegal migration across the Mediterranean and through the Balkans.

The “migration pact” seeks to accelerate the processing of asylum applications as well as enables the detention of asylum seekers who have a lower chance of successful bid at the EU's external borders.

Controversially, it also sets up a burden-sharing mechanism that will require the bloc's 27 member states to take in their fair share of migrants landing in just a handful of countries, such as Greece and Italy.

Countries like Poland and Hungary, which have rejected resettling asylum seekers, will be forced to pay a levy to help finance the system for more willing capitals.

At a debate ahead of the EU elections, Ursula Von der Leyen, the European Commission's president, last night rejected that her centre-right European People's Party was pushing a Rwanda-style plan for the bloc.

The top eurocrat, who is vying for a second term in office, went as far to suggest deporting migrants to the African country was a breach of international law.

“This is the UK, and we have nothing to do with it,” she told the audience.

“The UK left the European Union. Let them discuss their issues and we discuss our issues. We have fulfilled our international obligations – and that's very important – in the past, we fulfil them today and we will fulfil them tomorrow. This is absolutely necessary to the Geneva Convention ... the European convention.”

She added: “But I also think it is in order to say that we Europeans are the ones who decide who comes to the European Union and under what circumstances, and not the smugglers and traffickers.

“Therefore, agreements with third countries, for example Tunisia or Egypt, is investing in their economy, investing in their education system to create legal, safe pathways for people to come, also for protection, but not to define for the smugglers and traffickers who comes to the European Union.”