Speaking at Prime Minister's Questions, Boris Johnson said the early data indicated vaccines were also effective against the Indian variant.
In a positive signal from the government about the possibility of future easing, Mr Johnson praised those in areas with high case loads of the Indian variant for coming forward for jab.
He said: "I want particularly in this context to thank the people of Bolton, of Blackburn and many other places who have been coming forward to get first and second jabs."
Analysis by ITV News Political Reporter Shehab Khan
With the recent spike in cases of the so-called Indian variant, Boris Johnson faces two big questions both of which, in some form or another, were a key part of Prime Minister’s Questions.
Should the UK’s border policy be stronger, and will this ultimately impact the government’s plan to ease restrictions completely by 21 June?
On the first, the Prime Minister was adamant that not only does the UK have one of the strongest border policies in the world but also that he was not keen on legislating to stop people travelling to countries on the government’s amber list.
As it stands it is “guidance” that is being offered to people about what constitutes an acceptable trip and it is ultimately your own decision about whether you go.
This, in truth, speaks to the liberal side of Johnson’s political beliefs, much of which he has had to compromise throughout the duration of the pandemic. But there is now a conscious effort to slowly move away from strict rules.
On the second broad question, the Prime Minister said that having looked at the latest data he believes that vaccinations are working against the Indian variant.
That, on the face of it, sounds like good news, especially given the latest spike in cases.
We are, however, still waiting for confirmation that the government’s roadmap out of the pandemic is on track, but having spoken to a handful of backbench Conservative MPs, they don’t seem too worried at this stage about this date slipping too dramatically.
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The announcement comes after confusion about the government's policy on international travel with ministers offering contradictory advice about travelling to amber list countries.
Labour leader Sir Keir Starmer attacked the government saying it "had lost control of the messaging".
He asked the Prime Minister "if he doesn't want people to travel to amber list countries, why has he made it easier for them to do so?"
Mr Johnson denied the claim saying "we have one of the strongest border regimes anywhere in the world".
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Mr Johnson added: "It is very clear... you should not be going to an amber list country except for some extreme circumstance, such as the serious illness of a family member.
"You should not be going to an amber list country on holiday.
"If you do go to an amber list country...we will enforce the ten day quarantine period.
"If you break the rules, you face very substantial fines."