It comes as the UK tells the EU to act like "grown-ups" amid the vaccine export row but how has the political row has unfolded so far?
What is the latest from the EU?
European Commission President Ursula von der Leyen threatened to block exports of jabs from the EU to countries with higher vaccination rates that do not offer reciprocal supplies of vaccine.
Under pressure over the bloc’s relatively poor vaccine rollout, she ramped up the rhetoric this weekend, saying the EU has the power to "forbid" exports.
She added: "That is the message to AstraZeneca."
The EU's vaccination campaign is lagging behind the UK's, with the bloc claiming AstraZeneca has "underproduced and underdelivered" on its contract.
Chief spokesperson Eric Mamer told reporters in Brussels on Monday: "The president has given our view of what the situation is and what are the objectives that we are following.
"This is not about banning vaccine exports, this is about making sure that companies deliver on their commitments to the member states and the European Union that are inscribed in the contracts that they have with us.
"Therefore, this is our objective, to make sure that the contracts that we have signed are respected.
"In that context, the president has said that, of course, we see that, actually, companies that manufacture doses in the EU have been exporting very widely – which is in itself a good thing – but that we want to see reciprocity and proportionality in these exports."
Why have these proposals been put forward by the EU?
The warning from the EU reflects growing frustration on the continent that the bloc is not getting the supplies it expected from AstraZeneca.
But the British-Swedish manufacturer has previously maintained that because the bloc signed its contract later than the UK, EU manufacturing facilities were still catching up.
How could this affect the UK’s vaccine supplies?
Around 10 million doses of vaccine, mainly the BioNTech/Pfizer jab, have crossed the English Channel to the UK, but Brussels has complained that no AstraZeneca doses have been sent in the other direction.
Reports have suggested the latest focus of the row is on AstraZeneca vaccines produced in the Halix plant in the Netherlands, with officials arguing they should be kept for the EU rather than allowed to be exported to the UK.
How is the rollout progressing in the EU and UK?
Just over 10% of adults have received a first dose of a coronavirus vaccine across the EU, according to the European Centre for Disease Prevention and Control, while in the UK, the figure is now over 50%.
What has the UK said about the vaccines row?
Government sources said Mr Johnson spoke to Ms von der Leyen, along with Dutch and Belgian prime ministers Mark Rutte and Alexander De Croo last week.
He may speak to other EU leaders over the coming days, the source added.
It comes as the UK celebrated “a record-breaking day for the vaccine rollout” in the UK after 844,285 jabs were given to members of public on Saturday.
Defence Secretary Ben Wallace hit back on Sunday by warning the manufacture of the Pfizer vaccine depends on supplies from the UK, amid reports its production requires lipid ingredients shipped from Yorkshire.
He told BBC One’s The Andrew Marr Show: "The grown-up thing would be for the European Commission and some of the European leaders to not indulge in rhetoric but to recognise the obligations that we all have."
On Monday, health minister Helen Whately MP warns the EU should "keep to the commitment" it made to the UK on vaccines.
"The European Union has made a commitment. Ursula von der Leyen committed to the Prime Minister that the EU would not block countries from fulfilling their contractual obligations to the UK," Ms Whately told ITV News.
She warns: "It's crucial that the EU stands by that commitment."
She added: "That commitment is the right thing for them to say, the right thing for them to do, and any alternative to that simply can't be a good thing for anybody.
"The right course of action is for every company to fulfil its contractual obligations, and for countries to support them in doing so.
"It would be fundamentally unhelpful for any country to try and stop parts of production that are happening in their country - these are complex global supply chains."
Have there been other disputes over vaccines?
In January, the EU briefly attempted to trigger Article 16 of the Northern Ireland Protocol of the Brexit Withdrawal Agreement to impose controls on vaccines.
But Brussels swiftly backtracked after coming in for widespread criticism over the move from London, Dublin and Belfast, which came as EU chiefs faced increasing pressure over delays to the rollout of its vaccination programme.