UK Prime Minister Boris Johnson said he was "hopeful" that international travel could resume from May 17 but that "some of the destination countries that people might want to go to" had difficulties with the pandemic.
"We don’t want to see the virus be reimported into this country from abroad," Johnson said.
Johnson added that vaccine passports - a health document showing whether you have previously been infected or received a COVID-19 vaccine - could be "part of the way that people deal with" international travel, emphasising that "all countries are looking at" them as a possibility.
Watch Boris Johnson's press conference here
But, Johnson ruled out the "COVID status" certificates as a part of easing out of lockdown.
"There is absolutely no question of people being asked to produce certification or COVID status report when they go to the shops or to the pub garden or to the hairdressers or whatever on Monday and indeed we’re not planning that for step three either May 17th," Johnson said.
He added that there were "complicated ethical and practical issues" with asking people to produce a COVID-19 vaccination certificate, as not everyone would be able to receive the vaccine due to health issues.
UK to stick to the roadmap of easing out of lockdown
The UK will continue easing out of lockdown from April 12, as they reopen shops, outdoor dining for restaurants and bars, hairdressers, zoos, and gyms, Johnson announced.
He said the country had met their tests for easing restrictions but urged against "complacency", pointing out that it is still unknown how strong the vaccine will shield against infections.
"We can see the waves of sickness afflicting other countries and we've seen how this story goes," Johnson said.
UK officials said however that the situation had improved greatly, with an average of 47 deaths per day down from a peak of around 1,300 deaths per day.
Overall, one dose of a coronavirus vaccine reduced symptomatic disease and hospitalisations, they added. Around 60% of the country's adult population has received a first dose of the vaccine.
Chris Whitty, England's chief medical officer, said that the vaccines were being rolled out at "a remarkable rate".
This virus, however, will be around for the foreseeable future and vaccines may need to be updated, officials emphasised.
Twice-weekly rapid testing to become available
As part of easing lockdown measures, people in England will have access to twice-weekly rapid coronavirus testing, the government announced on Monday ahead of the expected briefing.
They hope that regular testing, along with vaccination, will help the country return to some kind of normalcy.
"Around 1 in 3 people who have COVID-19 show no symptoms, and as we reopen society and resume parts of life we have all dearly missed, regular rapid testing is going to be fundamental in helping us quickly spot positive cases and squash any outbreaks," health secretary Matt Hancock said in a statement.
According to the US Centres for Disease Control and Prevention (CDC), however, rapid tests, while fast, sometimes give incorrect results.
Dr Susan Hopkins at Public Health England says that rapid tests are a tool that can help the government "find COVID-19 cases that we wouldn’t otherwise know about, helping to break chains of transmission."
So far, more than 31 million people in the country have received a first dose of a COVID-19 jab.