People should not get "carried away with over optimism" after the UK approved its first coronavirus vaccine, Boris Johnson warned.
The PM said it does not mean "our struggle is over" and parts of the economy still face tough restrictions.
England's deputy chief medical officer Jonathan Van-Tam urged the public to be "patient and realistic" over the rollout of the Pfizer/BioNTech jab.
"It's going to take months, not weeks," he said.
Speaking at a Downing Street news conference, Mr Johnson said the decision to approve the Pfizer jab by regulator MHRA came amid "immense logistical challenges" in getting doses to vulnerable groups.
"It's going to continue to be tough for some sectors - but until the vaccine is deployed our plan relies on all of us making sacrifices to protect the ones we love," he said.
Prof Van-Tam admitted to being emotional after the UK became the first country to approve the Pfizer vaccine, but he too warned social-distancing rules would have to remain in place.
"If we relax too soon it will create a tidal wave of infections," he said.
"I don't think we are going to eradicate coronavirus ever. I think it's going to be with humankind forever," he added.
NHS England chief executive Sir Simon Stevens told the news conference the current plan would see the vaccine rolled out to 50 hospital hubs in England, with the over-80s, care home staff and front-line NHS staff being the first to receive it from next week.
Sir Simon said vulnerable people with outpatient appointments already scheduled are likely to be the very first to be offered the jab.
And he added all those vaccinated from next week will only be protected after a second dose in January.
The NHS is "raring to go" to vaccinate people in care homes, hopefully this month, Sir Simon said.
Prof Van-Tam said those offered the vaccine "must take it". "We need people to take it. This vaccine isn't going to help you if you don't take it," he said.
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