The Government’s Global Travel Taskforce will reconvene to issue a report by April 12 recommending how international trips can be safely facilitated.
Mr Johnson said this will “give people time to make their plans for the summer”.
Tui reported that they had had their best day of bookings in more than a month ahead of the summer, with strong interest in Greece, Spain and Turkey.
Watch: Should I book a holiday in 2021?
Thomas Cook told the BBC that bookings were "flooding in" for countries like the Dominican Republic, Greece, Cyprus and Mexico.
EasyJet also reported a 337 per cent surge in flight bookings, according to the broadcaster.
It saw a 630 per cent jump in holiday bookings for locations like Alicante, Malaga, Palmo, Faro and Crete. Bookings are strongest in August, followed by July and then September.
Travel industry leaders have expressed relief at the prospect of people in England being allowed to take summer holidays.
Mark Tanzer, chief executive of travel trade organisation Abta, said summer holidays will be crucial for both “travel businesses whose revenues have been wiped out” and for “millions of people who are desperate to travel again”.
But he urged Chancellor Rishi Sunak to use next month’s Budget to provide “tailored financial support” to travel agents and tour operators to enable them to “come through the weeks ahead”.
Paul Charles, chief executive of travel consultancy The PC Agency – who co-founded the Save Our Summer campaign, said the announcement was “the news the travel sector really wanted”.
He went on: “It means more consumers can be reassured that their 2021 summer trip can take place, or they can get a refund or refix their travel date.
“They can book knowing that this summer will be even safer than last.
“We will need to see the finer details in the future reviews for the sector’s restart but the Prime Minister’s comments are certainly far more positive and realistic than those made by some ministers just two weeks ago.”
Earlier this month, Transport Secretary Grant Shapps said foreign holidays will remain banned until “everybody” has had a coronavirus vaccine.
Watch: It is 'too soon' to book a summer holiday, says Transport Secretary Grant Shapps
His comments sparked an angry response from the travel industry, which accused him of undermining consumer confidence.
British Airways chief executive Sean Doyle said it is “critical we start looking at a way to restart travel”, adding that he is “pleased the Government has acknowledged that”.
He went on: “We support a data-led approach that protects public health. We want to work with Government’s taskforce on a road map now to ensure that aviation is in a strong position to support the UK as we emerge from the pandemic.”
Tim Alderslade, chief executive of trade body Airlines UK, said: “We’re grateful to the Prime Minister and Department for Transport for providing the clarity the whole sector was looking for that international travel can reopen this summer, as soon as it is safe to do so.
“This will provide much-needed reassurance not only to airlines in desperate need of a summer season but families looking to visit friends and family and take a long-awaited holiday, and we know there is enormous pent-up demand for when we can restart operations.”