Boris Johnson has warned the effects of a third wave of coronavirus will “wash up on our shores” from Europe.
The PM said the UK should be “under no illusion” we will “feel effects” of growing cases on the continent.
One of his ministers, Lord Bethell, also warned the UK might put “all our European neighbours” on the red list of countries, where arrivals are either banned or put in quarantine hotels.
The comments come amid a row over Covid-19 vaccine supplies in the EU.
The president of the European Commission, Ursula von der Leyen has warned the EU could “forbid” doses made in the bloc from being exported to the UK.
EU leaders will hold a virtual meeting on Thursday to discuss their plans.
Officials confirmed the PM spoke to German Chancellor Angela Merkel and French President Emmanuel Macron on Sunday about the ongoing issue, which would affect exports of the Oxford-AstraZeneca vaccine made in Europe.
Mr Johnson said he “talked to EU friends repeatedly” during the pandemic and had been “reassured… over the last few month they don’t want to see blockades”.
Downing Street also said President von der Leyen, had told Mr Johnson earlier this year that the EU was not intending to restrict exports of vaccines.
EU legislation allows measures to be taken “if severe difficulties arise in the supply of certain products” – which, in theory, could include export bans and the waiving of patent and intellectual property rights on vaccines.
But earlier, Mrs von der Leyen’s chief spokesman, Eric Mamer, insisted that Brussels was not seeking to ban vaccine exports, but wanted pharmaceutical firms to meet their contractual obligations to the bloc.
Mr Mamer said: “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.”
Asked if he was worried about the row, Mr Johnson told reporters: “I am reassured by talking to EU partners over the last few months that they don’t want to see blockades.”
But he went on to issue a warning about what the growing infections in Europe could mean for the UK.
The PM said: “On the continent right now you can see, sadly, there is a third wave under way.
“And people in this country should be under no illusions that previous experience has taught us that when a wave hits our friends, I’m afraid it washes up on our shores as well.”
He added: “I expect we will feel those effects in due course. That’s why we’re getting on with our vaccination programme as fast as we can.”
Later, Health Minister Lord Bethell warned how the rising cases and issues with vaccines could affect travel to European countries going forward.
He told the House of Lords: “I don’t know how that will play out and it’s certainly above my pay grade to speculate, but we are all aware that the possibility lies that will have to red list all of our European neighbours – but that would be done with huge regret.”
On Monday, the UK reported 17 deaths over the last 24 hours of people who had tested positive for Covid-19 in the past 28 days.
A further 5,342 cases were also confirmed, while another 367,006 people received their first vaccination – along with 52,612 who got their second jab.
Meanwhile, the long-awaited results of the US trial of the Oxford-AstraZeneca vaccine, which involved more than 32,000 volunteers, show that the jab is safe and highly effective.
Several European leaders paused rollout of the vaccine amid concerns of a possible link with blood clots. UK and EU regulators said there was no evidence the vaccine causes blood clots.
European leaders have faced criticism for the slow pace of the vaccine rollout on the continent.
Less than 12% of the EU’s population is reported to have received the vaccine, compared with nearly 40% in the UK – although the bloc has 446 million citizens, compared to almost 67 million in the UK.
The EU has encountered production problems with the Pfizer-BioNTech, Moderna and Oxford-AstraZeneca vaccines.
British-Swedish manufacturer AstraZeneca said the fact that EU contracts were signed later than with the UK caused problems with supplying their vaccine.
Downing Street has previously said that it does not believe that vaccine supply issues will affect the current road map for easing lockdown restrictions.
Irish Taoiseach Michael Martin said it is vital that supply chains were kept open, telling RTE: “Once you start putting up the barriers, other people start putting up barriers globally and it could lead to everybody losing. We’d all lose in that situation.”
Labour leader Sir Keir Starmer also said the UK government was right to say that contractual obligations need to be honoured, telling LBC that the EU was not “helping itself”.
The Guardian says a report by data analysts Airfinity suggests that if an export ban was applied to all vaccines – including those from Moderna and Johnson & Johnson that have yet to be deployed in the UK – it would see the offer of a first vaccine to every adult completed in late August rather than the target date of 31 July.
But Mr Johnson said the UK had already vaccinated over half of the adults in the country, adding: “We’ll just bash on with the road map we’ve set out.”
The prospect of a third coronavirus wave won’t engulf anyone with joy. So why did Boris Johnson highlight this danger today?
Privately and publicly ministers are making it clear that they don’t want to delay the dates in England’s roadmap out of lockdown.
There will be a vote in Parliament on coronavirus restrictions later this week.
So by stressing the risk that the virus still poses, the PM may be hoping to convince restless backbenchers that he can’t go any quicker.
He may also be trying to persuade vaccinated people with itchy feet that booking spring or summer holidays would still be premature.
He is preparing us, too, for the strong possibility that cases could rise in the coming weeks – not just because of “incoming” risks, but because rules here are being slowly relaxed.
But by stressing the shared threat from the coronavirus – i.e. the sooner the EU population is vaccinated, the less chance of importing a third wave – his comments could be also be clearing the way for more UK/EU vaccine co-operation, and the dousing down of an inflammatory row with Brussels.
The latest point of contention between the UK and the EU appears to be over vaccine doses being manufactured at a plant in the Netherlands.
An EU official told Reuters news agency that those doses should be distributed among member states, and not sent to Britain.