Speaking at Prime Minister's Questions, the PM said people must "get used to the idea of vaccinating, then re-vaccinating in the autumn as we come to face these new variants".
He added that the government had secured 50 million doses of a vaccine developed by CureVac, "because we believe that may help us to develop vaccines that can respond at scale to new variants of the virus".
He said there are "measured [and] proportionate" rules in place at the UK's borders to ensure no foreign variants are brought to the UK, which are "getting tougher" from Monday.
Labour leader Sir Keir Starmer said the PM should "secure our borders with comprehensive hotel quarantine on arrival", suggesting new border controls should go further.
On Monday, a new set of rules will come into force for arrivals to the UK, with anyone travelling from red list countries, where variants of concern have been identified, required to quarantine in a hotel for ten days before being allowed to leave isolation.
A range of other measures will be brought in, and a number of punishments including the threat of jail time, for those who break the rules.
Sir Keir said the prime minister is "failing to give security to British business and is failing to secure our borders", as he urged him to extend financial support.
He suggested an extension of furlough, business rates relief and VAT cuts for hospitality.
The prime minister said his opposite number should wait for Chancellor Rishi Sunak to set out the next Budget in March, and sarcastically welcomed Sir Keir's support for business.
He said: "I'm delighted to hear this enthusiasm for business from the Labour Party when they stood on a manifesto to destroy capitalism at the last election."
He added: "What I hope very much is that we may hear from the right honourable gentleman opposite that he has not only has a Damascene conversion to the importance of business but a Damascene conversion to supporting all the government's policies... rather than sniping from the sidelines why doesn't he get behind us and back the Government, back us in our efforts to back business and back the British people?"
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Sir Keir hit back: "I'm not going to take lectures from a man who wrote two versions of every column he ever wrote as a journalist, proposed Donald Trump for a Nobel Peace Prize and gave Dominic Cummings a pay rise."
He accused Mr Johnson of appearing to "change policy pretty well every day" on decisions over securing the UK border against Covid-19 variants, adding Oxford University research suggests the country lags behind others when it comes to such restrictions.
Sir Keir went on: "Fifty days after we first discovered the South African variant, how does the Prime Minister explain that?"
Mr Johnson replied: "There are some countries in Europe which don't even have a hotel quarantine scheme such as the one we're putting in on Monday. We have amongst the toughest border regimes anywhere in the world."
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