On Monday, the EU Commission published a series of proposals in an attempt to ease the implementation of the Northern Ireland Protocol. However, the UK Government rejected the proposals and said there insufficient for the scale of the problems.
A Downing Street spokesperson said the two sides needed "comprehensive and durable solutions".
He said: "We need comprehensive and durable solutions if we are to avoid further disruption to everyday lives in Northern Ireland."
However, he said what the EU proposed represented "only a small subset of the many difficulties caused by the way the protocol is operating".
The spokesperson continued: "The EU's proposal was a welcome start but it would be complex to operate, onerous and would not deal at all with those medicines, such as new cancer drugs, which under current arrangements must be licensed by the European Medicines Agency in Northern Ireland."
Brexit minister Lord Frost threatened to trigger Article 16 of the agreement unless there were major changes to the legal text of the protocol.
Last week, Commission chief Ursula von der Leyen said the EU "will not renegotiate" the withdrawal agreement the Prime Minister signed in December.
She said: "The EU will continue to be creative and flexible within the Protocol framework. But we will not renegotiate.
"We must jointly ensure stability and predictability in Northern Ireland."
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The Northern Ireland Protocol is designed to avoid customs checks along the Irish border.
To avoid a hard border, Northern Ireland effectively remains in the EU’s single market, with a number of controls on goods shipped from mainland Britain.
Last month, the two sides agreed on an extension to the amnesty on chilled meats moving between Great Britain and Northern Ireland.
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This latest amnesty will now expire in September, with both sides continuing to negotiate on a long-term solution.
Trust was badly damaged in January when the EU moved to block the export of COVID-19 vaccines to Northern Ireland.
Tensions across Northern Ireland reached boiling point and the nation was rocked by street violence in April.
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12.10pm update: 'Red tape cut' Wine dealer highlights money Brits can save on imports amid price raise
Red tape plans for British wine imports have been scrapped in new post-Brexit government plans which spells good news for British businesses, according to wine merchant Jasper Corbett.
Speaking to GB News' Nigel Farage, Mr Corbett explained how the cutting of potential red tape placed on wine by the British Government has saved Brits spending more for their vino.
The wine merchant explained how the Government have decided to scrap earmarked post-Brexit wine checks on wine imports, which involve wine tests to check for acidity on each import, which could have made bottles of wine 10-15p more expensive for Brits.
He said the U-turn by the government to not go ahead with the VI-1 certificates was good news for both merchants and consumers, saving Britons around ￡130 million.
Mr Farage said how the move is a "Farage dream" of cutting red tape.
11.45am update: Same old Labour! Starmer looks to bind Britain to EU beyond Brexit as he demands new deal
Labour is demanding Boris Johnson push for a new Brexit deal that would see the UK bound by EU rules indefinitely.
Shadow chancellor Rachel Reeves is pushing for ministers to cave to EU demands on a compromise over the Northern Ireland Protocol.
Lord Frost is seeking to renegotiate the Brexit mechanism, warning London and Brussels "cannot go on as we are" with the current deal.
Ms Reeves admitted Labour also believes the Protocol requires reform and wants Lord Frost to bow to the EU's suggestions.
"We thought the deal would be built on, but gaps have not been filled in," Ms Reeves said as she criticised Boris Johnson's "thin" Brexit deal.
10.35am update: Barack Obama thanked for Brexit referendum victory: 'Boris scoffed at him!'
Barack Obama's visit to Britain ahead of the 2016 EU referendum helped the Vote Leave camp swing the vote in their favour, Lord David Owen told Express.co.uk.
Two months before the Brexit referendum, former US President Barack Obama visited London.
Speaking in a press conference alongside former Prime Minister David Cameron, Mr Obama warned Britons that a trade deal with the US would have not been a priority if the country left the EU.
Mr Obama said: “The UK is going to be at the back of the queue.”
10am update: ‘Admit you were wrong!’ Nexit calls erupt as Brexit Britain’s economy booms against EU
Brexit Britain's economy may grow exponentially compared to the EU's by the end of this year, economists claim, sparking calls for the Netherlands to leave the bloc.
Nexit Denktank campaigners are urging the Dutch government to allow for a referendum on the Netherlands' membership to the EU, arguing Brexit Britain is a great example of life outside the bloc.
The Dutch campaigners are calling on anti-Brexit fearmongers to admit they were wrong about the catastrophic predictions made ahead of the 2016 UK referendum as they cite the latest economic figures proving Britain's success.
8.50am update: Boris Johnson can secure bumper US trade deal with Biden by copying Australian tactic
Boris Johnson has been told he can seal a bumper post-Brexit trade deal with the US by adopting a straightforward approach to negotiating which emphasises the importance of deadlines.
Former Tory and UKIP MP Douglas Carswell told Express.co.uk: “When Britain and Australia sat down and created a new trade deal I think people were quite surprised at how quickly it can be done.
“And I think this is all because of what you might call the Tony Abbott lesson.
“Tony Abbott is the former Australian prime minister, and he has a key role advising the UK Government.
“Now one of the great bits of advice Tony has always given people is that when you want to do a trade deal, set your officials a hard deadline for negotiation because he learned that the negotiations will always expand to fill the time allotted to them.
“Bear in mind, as always, right now, even without a trade deal, America is our single largest trade partner and our single largest source of foreign investment.
“We're massive trade partners with each other so we're not starting from a completely blank canvas.”
8.30am update: Brexit outrage: EU accused of having 'head in sand' – anger at 'belligerent' revenge plot
Arlene Foster claimed that the EU "has its head in the sand" over border issues in Northern Ireland and will continue "its belligerent attitude to the protocol".
Ms Foster claims the present circumstances in Northern Ireland should see the implementation of Article 16 of the protocol.
The former leader of the DUP claimed in a piece written today in the Daily Telegraph that there was a "well-worn mantra of the protocol protecting the peace in Northern Ireland" emanating from the EU.
However, the unionist politician suggested instead that "the protocol does not protect the Good Friday Agreement".
8am update: Brexit fury: Switzerland provides warning to UK for 'war of attrition' with EU
Brexit tensions between the UK and EU could follow a similar route to the dispute between Brussels and Switzerland, an expert tells Express.co.uk.
Kevin Featherstone, an academic at the London School of Economics, points to Switzerland as an example of how grappling with the EU can last a long time.
He said: "I think what we have, at least for the medium term, we are going to have continued friction between the UK and the EU27.
"Why is that? It's a direct consequence of us not being able to reach an overarching agreement that sets out all the substance and details.
"What we have is a pure outline agreement that can be interpreted differently.
"Because of that, it always meant Brexit would be a source of conflict between Brussels and London."